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Lynna [10]
3 years ago
13

Write the equation of the hyperbola with foci at (1, 5) and (7, 5) and with vertices at (2, 5) and (6, 5).

Mathematics
1 answer:
mash [69]3 years ago
6 0
If you plot the points given on a coordinate plane you see that this is a hyperbola that is is horizontal in nature, meaning it opens side to side, not up and down.  We can determine the center of it by taking the point equidistant from the vertices, which is (4, 5), the h and k of our center, respectively.  Also, the equation looks like this when it is horizontal: \frac{(x-h) ^{2} }{ a^{2} } - \frac{(y-k) ^{2} }{ b^{2} } =1.  a is the distance between the center and the vertices, so our a = 2, and c is the distance between the center and the foci, so our c = 3.  We need to find b now, using Pythagorean's theorem.  ( 2)^{2} + b^{2} =( 3)^{2} and b= \sqrt{5}.  Now we have everything we need to rewrite the equation: \frac{(x-4) ^{2} }{4} - \frac{(y-5) ^{2} }{5} =1
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Answer:

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Step-by-step explanation:

<u>Given points </u>

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<u>Use slope formula to find the slope</u>

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|-4| - 8 + 10 = ???<br> answer for points
Elis [28]

Answer:

6

Step-by-step explanation:

As you might know, the two lines surrounding the -4 represent the absolute value, which is basically the distance from 0, and the distance is always positive. To clear any confusion, the absolute value of positive number will not be it's opposite because remember, distance is always positive, so absolute value is always positive (because it is basically the distance from zero).

To help, here is an example (that is not related to the problem!):

|-6| = 6

|6|  = 6

<em>Now, back to the problem...</em>

Since you now know that the absolute value is always positive, |-4| would equal 4. So now you have:

4 - 8 + 10 = ???

From here, you can just solve and the answer is 6, so:

4 - 8 + 10 = 6

You final answer is 6.

Hope this helped somehow :D

4 0
3 years ago
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maxonik [38]

Answer:

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Step-by-step explanation:

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x = 11

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