Question

Please help !!! WILL MARK BRAINLIEST! +50 points!

Answer 1

Fun!

The center of the hyperbola is the midpoint of its foci.  The distance between the foci is 43-9=34.   So they're 17 from the center.

We have coordinates

F1(0,17)

F2(0,-17)

Let's call the vertex of the hyperbola V.   We have

V(0,13)

This is a vertical hyperbola so the equation is of the form

$\dfrac{y^2}{a^2}- \dfrac{x^2}{b^2}=1$

The vertices for a vertical hyperbola like this are (0, a) and (0,-a)

So we have a=13

The distance c from the foci to the center is given by

$c^2 = a^2+b^2$

$b^2 = c^2-a^2 = 17^2 - 13^2 = 120$

That says our hyperbola's equation is

$\dfrac{y^2}{169}- \dfrac{x^2}{120}=1$

That's our answer.