Question

Find the foci of the hyperbola defined by this equation: ((x-4)^2)-(1)-((y+4)^2)-(9)=1

Answer 1

\[\frac{(x-4)^2}{1}-\frac{(y+4)^2}{9}=1\]

Answer 2

Is that the problem?

Answer 3

yes

Answer 4

\[\frac{(x-h)^2}{a^2}-\frac{(y-k)^2}{b^2}=1\]

Answer 5

That is the equation of a hyperbola with center (h,k)

Answer 6

ok

Answer 7

a^2+b^2=c^2

Answer 8

So identify a^2 and b^2 and use them to find c because the foci are c units to the right and c units to the left of the center.

Answer 9

I don't know how to do that....

Answer 10

What is a^2?

Answer 11

1^2

Answer 12

The number in your equation that replaces a^2 is 1

Answer 13

What is b^2?

Answer 14

9

Answer 15

Now take the equation I posted. Replace a^2 with 1. Replace b^2 with 9. Solve for c

Answer 16

10?

Answer 17

c^2=10 so c is sqrt10