What is the equation of the hyperbola with foci (0, 10), (0, ?10) and vertices (0, 6), (0, ?6)

Answers

Answer 1

As given,

Foci (0,10) ; (0,-10) and Vertices (0,6) ; (0,-6)

Now we know the general equation of hyperbola will be,

[tex]\frac{y^{2} }{a^{2} } -\frac{x^{2} }{b^{2} } =1\\\\[/tex]

Now distance from origin to vertex is given, 6 ;

therefore, [tex]a=6[/tex]

And distance from origin to Focus is given , [tex]c=10;\\[/tex]

Using the equation, [tex]c^{2}=a^{2}+b^{2} \\c=10 ; a=6,[/tex]

Apply these values in the equation and find out the value of b,

[tex]c^{2}=a^{2} +b^{2}\\10^{2}=6^{2}+b^{2}\\100=36+b^{2}\\100-36=b^{2}\\ b^{2}=64\\ b=8\\[/tex]

Hence equation of Hyperbola will be,

[tex]\frac{y^{2} }{6^{2} }-\frac{x^{2} }{8^{2} }=1\\\frac{y^{2} }{36}-\frac{x^{2} }{64} =1[/tex]

Here we are done.

Answer 2

Answer:

y^2/36 - x^2/64 = 1

Hope this helps <3


Related Questions

Compared with the cost of tuition, fees, and books for a traditional college course, the cost of a CLEP exam is:

Answers

The answer to the question is: significantly lower

Answer:

much lower.

Explanation:

basically the same answer but it has different wording now

_________ of the population of the United States is obese. A. 10% B. 25% C. 33% D. 50% Please select the best answer from the choices provided. A B C D

Answers

The best answer is C, 33%. Normally I would explain why, but luckily for you this is just a simple fact question. I did some research myself and it turns out men in the United States are 32.2% fat, and the woman are 35.5%.

Hopefully my answer is useful to you. Please mark brainliest if useful to you. You can do it!

33% of the population of the United States is obese. Thus the correct answer is C.

What is the population?

The term population refers to the number of people living in a country or particular location. Generally, the population will be calculated on living organisms living in the area. For an example, the population of the United, states is 329.5 million as of 2020.

Situation of obesity refers to excessively fat present in the body which can cause risks to life and danger to well-being. The most cause of obesity is sedentary or inactive lifestyle of an individual.

According to the evidence more than one-third people of in America is under the category of obesity which decreases the average health of an Adult in the country leads to chronic diseases and disturbs the health of the country.

Therefore, option C 33% is appropriate.

Learn more about the population, here:

https://brainly.com/question/27991860

#SPJ2

Trey has answered 15 E-mails. This is 20% of E-mails he must answer. How many E-mails does he need to answer? Pls help hkhxdfsrwhetwjeykrutiyuoui;op';kljkthyjrtherweqwertyuilo;p'[o;pio;uiylutryte

Answers

ANSWER:

75 emails.

Trey has to answer a total of 75 emails.

STEP-BY-STEP EXPLANATION:

If:

20% of emails = 15

Then:

20% × 5 = 15 × 5

100% of emails = 75

easy peasy math (i do math weird in my hea so hopefully i convey this in a way you understand as well)


if 15 is 20% of the total emails he has 80% left right.

20% is 1/5 so you need to find the other 4/5

to do this you take the 1/5 ammount (15) and times that by 4

so thats  15 times 4

which is 60

he has 60 emails left



if the question is how many he has left then the answer is 60

if the answer is how many total emails then you add the 15 hes answered already to the 60 he needs to answer still and its 75

Spider crabs live in the shallow regions of the ocean floor. Algae tend to grow on the surface of spider crabs. The algae provide the crabs protection from predators by camouflaging them. The spider crabs give the algae shelter. What does this description suggest?
1. The algae are parasites of the spider crabs.
2. The algae and the spider crabs have a mutualistic relationship.
3. The spider crabs are commensals, and the algae are parasites.
4. The spider crabs benefit from the algae living on them.
5. The spider crabs are parasites of the algae.

Answers

the given description suggests that the algae and spider crabs have a mutualistic relationship that is benefiting each other.

The algae and the spider crabs have a mutualistic relationship.

Option 2

Explanation:

A mutualistic relationship is a relationship where two organisms from different species work in cohesion symbiotically and benefit each other by it. Normally, such organisms evolve to accept each other symbiotically because they have been a part of each other’s environment in the later times.

They have adapted to be working together for sustaining their life and becoming beneficiaries for each other in the process and continuing the same for a long period. A basic example of such a relationship is of a bee and a flower.

Prompt
What is your personal ideology? Give your opinion on the three following topics. Justify your support or opposition to each issue by using examples. Issue one: should the government have the right to place a high tax on soda to discourage its consumption and fight teen obesity? Issue two: should the government be allowed to monitor your actions on the internet to keep the nation safe from terrorism? Issue three: should the government be allowed to outlaw texting while driving to keep drivers safer on the road?

Answers

Issue one: The government should not have the right to issue a higher tax on carbonated drinks/soda to discourage teen obesity because it would be not alter the demand for these types of products. Say for example we use the supply, demand, quantity and price model, supply and quantity are unaffected in this model, whilst price goes up. When the price goes up, this would be an example of where demand does not decrease since the price would not deter people from purchasing it. With the amount of sodas that have to be regulated and how common they are to the everyday life, it'd be a waste of time. Furthermore, it is not the responsibility of the government to regulate personal choices done by the customers, it is their own choice if they choose to be healthy or not.


Issue two: The government does not have the right to monitor our actions on the internet to keep the nation safe from terrorism. The internet is a free market, a public entity supplied by public cooperations and access given by ISPs. The government's jurisdiction does not give them permission to monitor the internet as it could possibly fall under a violation of the fourth amendment. The ISPs, social media networks, and any other cooperation has the right to monitor actions as it'd be written out and agreed by the user in their terms of service, the government should not have involvement, only their intervention is required when a report is filed.


Issue three: The government should be allowed to outlaw texting while driving since it is a hazard to personal safety and the safety of others. The roads in the United States of America are mostly public, and texting while driving impairs the user's ability to react to incoming situations, whilst taking their focus off the road. Similar to drinking while driving, it only becomes an issue when the safety of others aside from your self is put at risk. In which case, I do believe the government has the right to outlaw texting while driving to keep drivers safer on the road.

A bacterium was found to contain a sequence of ATCGGGATCCT in its genome. A few generations later, the sequence was found to be ATCGGGGGGATCCT. What type of mutation caused this change in the bacteria?
A.
duplication
B.
insertion
C.
inversion
D.
translocation

Answers

Answer:

duplication  

Explanation:

Inversion

If we talk about inversion, it inversion, it is a process in which a specific base sequence is inverted or rearranged in such a way that direction is reversed. For example: ABC is changed into BCA, therefore it is not right option.

Translocation

If we talk about translocation,it is  caused by rearrangement of parts between non homologous chromosomes. It can be balanced or unbalanced but it involves two genes or two sets of chromosomes. But in our example, we have only one sequence of DNA under study, therefore, inversion is not possible.

Insertion

Talking about insertion, it involves addition of one or more nucleotide at certain position of gene sequence. There are chances that it can be an insertion of GGG but the insertion of three G instead of any random nucleotide addition or nucleotide sequence addition is rare. So, there are less chances that this is an insertion and more chances that this is an exact duplication event.

Duplication:

If we talk about duplication, a certain portion of a gene or chromosome is  replicated or duplicated in such a way that it results in more than one copies of that region.

Keeping that definition infront, we see that GGG duplicated to GGGGGG.  So, if we logically look at the question, duplication seems to be the most appropriate option.

Hope it help!

Answer:

duplication

Explanation:just did it and got it right.

A box contains 40 number tiles numbered 1 to 40. If a tile is drawn at random, what is the probability that the number drawn is a multiple of 3 or 4? Find P(Multiple of 4 or Multiple of 5)

Answers

Explanation 1 P (3 or 4):

There are 40 number tiles numbered 1 to 40.

Multiple of 3 in 1 to 40 are:

There are 10 multiples till 30 (since [tex]3 \times 10 = 30[/tex]) and then 33, 36, and 39 are other three multiples till 40. So there are 13 multiples of 3 from 1 to 40.

Multiples of 4 in 1 to 40 are:

There are 10 multiples till 40 (since [tex]4 \times 10 = 40[/tex]) . So there are 10 multiples of 4 from 1 to 40.

Common Multiples of 3 and 4 in 1 to 40 is,

12, 28, 36, only 3

So, the probability of 3 or 4 is,

[tex]P(\text {mult of 3})+P(\text {mult of 4}) -P(\text {mult of 3 and 4})[/tex]

[tex]=\frac{13}{40} +\frac{10}{40} -\frac{3}{40}[/tex]

[tex]=\frac{23}{40} -\frac{3}{40}[/tex]

[tex]=\frac{20}{40}[/tex]

[tex]=\frac{1}{2}[/tex]

So the probability of 3 or 4 is [tex]\frac{1}{2}[/tex].


Explanation 2 P(4 or 5):

Multiples of 4 in 1 to 40 are:

There are 10 multiples till 40 (since [tex]4 \times 10 = 40[/tex]) . So there are 10 multiples of 4 from 1 to 40.

Multiple of 5 in 1 to 40 are:

There are 8 multiples in 40 (since [tex]5 \times 8 = 40[/tex]). So there are 8 multiples of 5 from 1 to 40.

Common Multiples of 4 and 5 in 1 to 40 is,

20 and 40 only 2

So, the probability of 4 or 5 is,

[tex]P(\text {mult of 4})+P(\text {mult of 5}) -P(\text {mult of 4 and 5})[/tex]

[tex]=\frac{10}{40} +\frac{8}{40} -\frac{2}{40}[/tex]

[tex]=\frac{18}{40} -\frac{2}{40}[/tex]

[tex]=\frac{16}{40}[/tex]

[tex]=\frac{2}{5}[/tex]

So the probability of 4 or 5 is [tex]\frac{2}{5}[/tex].

A fish fossil is found in a rock. A foot bone and tooth are found in an older layer of the same rock. What can scientists learn from the rock? A) The area changed from land to water. B) The area changed from water to land. C) The area has always been land. D) The area was once an ocean.

Answers

A) The layer changed from land to water

=> From the fossil of the fish, we can say that the fish used to live in that area From the other fossils, we can tell that land animals lived there first before the fish appear due to the fact that the layer cointaining the bone and tooth is older -> that layer appeared first, which can only mean one thing: that area changed from land to water.

Answer:

A fish fossil found in a rock. A foot bone and tooth are found in an older layer of the same rock. What can scientists learn from a rock?

Explanation:

The area changed from land to water.

How are 3-D printers useful in studying evolution?
A.
to color the fossils of organisms
B.
to create clones of extinct organisms
C.
to create replicas of fossils
D.
to prepare paper cutouts of organisms
E.
to study the composition of fossils

Answers

They will be useful to create replicas of fossils




Mind marking me brainliest. Thank you!

Answer:

For those of you still looking for the answer its to create replicas of fossils

Explanation:

Other Questions
Whose beaker has the least amount of liquid in it.Jay 0.8Alana 1.05Evan 1.2 Stacey 0.75 Erica has 1 over 3 of a watermelon to share equally with 3 friends. How much will each person get What do you like or not like about Theodore Roosevelt? Do you agree or disagree with his domestic and foreign policies? What is your opinion of his attitude toward foreign nations and peoples? Do you agree or disagree with his methods of achieving his goals for the United States? Be as detailed as possible. Find the measure of angle x in the diagram below.A. 25B. 45C. 105D. 145 properties of isoceles trapezoids?? the arthur most likely italicized ghe word green in the first paragraph because please help Question 1 (20 points)Newton's ____________ Law of of motion states that every action has an equal and opposite reaction.Question 1 options:1st2nd3rdnoneQuestion 2 (20 points)2. Air is forced from the bottom of a rocket and its liftoff. The force causing the rocket to liftoff is a(n)?Question 2 options:reaction forcecombined forceaction forcenone of the aboveQuestion 3 (20 points)3. Equal and opposite forces that act on an object are called?Question 3 options:dual forcesbalanced forcesunbalanced forcesground forcesQuestion 4 (20 points)4. An example of an action and reaction is sitting on a chair. Your body pushes down on the chair because of the force of ______________________. and the chair pushes up on your body with an equal force (normal force)Question 4 options:inertiagravityfrictionnone of the aboveQuestion 5 (20 points)5. Action and reaction always act on the same object.Question 5 options:TrueFalse Constructive interference occurs when the crests of one wave overlap the crests of another wave. What is the result of constructive interference? A. decreased frequency B. increased frequency C. decreased amplitude D. increased amplitude What transformations change the graph of f(x) to the graph of g(x)? f(x) = 3x2 g(x) = 9x2 - 4 Question 2 options: The graph of g(x) is the graph of f(x) stretched vertically by a factor of 1/3 and translated up 4 units. The graph of g(x) is the graph of f(x) stretched vertically by a factor of 1/3 and translated down 4 units. The graph of g(x) is the graph of f(x) stretched vertically by a factor of 3 and translated up 4 units. The graph of g(x) is the graph of f(x) stretched vertically by a factor of 3 and translated down 4 units. Based on what the HIV tests are testing for, why is it recommended to go back and retest for HIV after three months? (Site 1) Two polygons are similar. The perimeter of the larger polygon is 85 meters and the ratio of the corresponding side lengths is [tex]\frac{2}{5}[/tex]. Find the perimeter of the other polygon. A person who weighs 120 pounds on Earth weighs 20 pounds on the Moon. How much does a 93-pound person weigh on the Moon? A person who weighs 120 pounds on Earth weighs 20 pounds on the Moon. How much does a 93-pound person weigh on the Moon? Item 22 A person who weighs 120 pounds on Earth weighs 20 pounds on the Moon. How much does a 93-pound person weigh on the Moon? Which change of state occurs at 100 C when heat energy has been added to liquid water? A.boiling B.melting C.freezing D.condensing How did the competing interests of scientists change thinking during the scientific revolution? And can i please get and educational answer that actually makes sense? 7) Days People 1 26 2 30 3 34 4 38 5 42 6 46 The chart shows how many people have signed up to go on a field trip each day. 62 students are allowed to go on the field trip. On which day would you expect that number to be reached? A) 8 B) 9 C) 10 D) f(x)=-x^2+1 find f(-3) what would happen if glycolysis could not happen in a cell? ) Gonorrhea can be treated with antibiotics. True False Question 1 (Fill-In-The-Blank Worth 1 points)Fill the blank with the preterite form of the verb in parentheses.Usted_____________ la computadora al trabajo . (traer)Answer for Blank 1:Question 2 (Fill-In-The-Blank Worth 1 points)Fill the blank with the preterite form of the verb in parentheses.Ustedes ___________ la comida a la fiesta. (traer)Answer for Blank 1:Question 3 (Fill-In-The-Blank Worth 1 points)Fill the blank with the preterite form of the verb in parentheses.Mario no ____________nada a clase hoy. (traer)Answer for Blank 1:Question 4 (Fill-In-The-Blank Worth 1 points)Fill the blank with the preterite form of the verb in parentheses.Yo no ____________mis libros. (traer)Answer for Blank 1:Question 5 (Fill-In-The-Blank Worth 1 points)Yo marco el nmero con los __________.Answer for Blank 1:Question 6 (Fill-In-The-Blank Worth 1 points)Mi amiga vive lejos. Hago la llamada de larga _________.Answer for Blank 1:Question 7 (Fill-In-The-Blank Worth 1 points)En espaol, "to pick up" el auricular es ________________.Answer for Blank 1:Question 8 (Fill-In-The-Blank Worth 1 points)Yo cuelgo el _______________Answer for Blank 1:Question 9 (Fill-In-The-Blank Worth 1 points)Cuando estoy en la calle, uso el __________celular.Answer for Blank 1:Question 10 (Fill-In-The-Blank Worth 1 points)Yo ____ el nmero con los botones.Answer for Blank 1:Question 11 (Fill-In-The-Blank Worth 1 points)Mi amiga no vive en mi ciudad. Ella vive muy lejos en Europa. Para llamarla, necesito hacer una llamada de _________ distancia.Answer for Blank 1:Question 12 (Fill-In-The-Blank Worth 1 points)Fill the blank with the preterite form of the verb in parentheses.Ricardo _________su nombre a la Seora. (decir)Answer for Blank 1:Question 13 (Fill-In-The-Blank Worth 1 points)Fill the blank with the preterite form of the verb in parentheses.Ustedes le ___________ el nmero al operador. (decir)Answer for Blank 1:Question 14 (Fill-In-The-Blank Worth 1 points)Fill the blank with the preterite form of the verb in parentheses.Yo _________la verdad. (decir)Answer for Blank 1:Question 15 (Fill-In-The-Blank Worth 1 points)Fill the blank with the preterite form of the verb in parentheses.Nosotros ____________ la verdad al profesor. (decir)Answer for Blank 1: Why are Theodore Roosevelt and Woodrow Wilson both considered to be "Progressive" Presidents?A)both were DemocratsB)neither advocated warC)neither supported business regulationD)they both believed government could make laws that responded to and prevented social problems Eliminate Steam Workshop Downloader