Question

Find the equation of the hyperbola with the following properties. Express your answer in standard form.Foci at (7, 0) and (7, 10)Asymptotes ofy -5 = t;( -7

Answer 1

`((y-5)^2)/(16)-((x-7)^2)/(9)=1`

Step-by-step explanation:

The standard form of an hyperbola is:

`((y-k)^2)/(a^2)-((x-h)^2)/(b^2)=1`

Where (h, k) are the coordinates of the center.

We are given the asyptotes and the foci.

The foci are (7, 0) and (7, 10)

The y value of the center of the parabola is midway from the two foci. Then, the y-coordinate of the center is 5

The coordinated of the center are (7, 5)

Now, we can use that the form of the asymptotes are:

`y=k\pm(a)/(b)(x-h)`

We have:

`y-5=(4)/(3)(x-7)`

Then:

`(a)/(b)=(4)/(3)`

a = 4

b = 3

Now we can write: