Question

Find the vertices and foci of the hyperbola with equation (x-5)^2/81 - (y -1)^2/48=1

Answer 1

I just need to know the steps or formula on how to find the foci.

Answer 2

do you know the center? you need that first

Answer 3

no I'm not sure :/

Answer 4

\[\frac{(x-h)^2}{a^2}-\frac{(y-k)^2}{b^2}=1\]
center is \((h,k)\)
\[\frac{(x-5)^2}{81}-\frac{(y-1)^2}{48}=1\]

Answer 5

center is \((5,1)\)

Answer 6

now you need to find \(c\) because the foci will be \(c\) units to the left and right of the center
that is why you need to know the center first

Answer 7

right, and in this case we use the a and b to find the c. is the a the larger denominator or the smaller one in this case?

Answer 8

use \(c^2=a^2+b^2\) in your case \(c^2=81+48=129\) and so \(c=\sqrt{129}\)

Answer 9

\(c^2\) is the sum of the two denominators

Answer 10

alright I'm with you so far :)

Answer 11

@satellite73 :/

Answer 12

@kropot72