Question

What are the foci of the hyperbola whose equation is

(-6, 2) and (14, 2)
(-4, 2) and (12,2)
(4,-8) and (4, 12)
(4,-6) and (4, 10)

Answer 1

I think the answer is D

Answer 2

(4,12) (4,-8)

Explanation:

you can find the distance from the foci to the center of a hyperbola using the formula c2 = a2 + b2.

in this equation we have both a and b, so substitute the values into the equation...

c2 = 64 + 36

c2 = 100

square root

c=10

therefore the distance from the foci from the center is 10 units.

since the equation has the y term first, the transverse axis is vertical. so 10 y units from the center which is (4,2) is (4,12) and (4,-8)

making the answer be (4,12) and (4,-8).

Hope this helped :)