Question

a hyperbola centered at (0,0) has vertices (0,+-6) and one focus (0,-10). what is the standard form of the equation of the hyperbola.

Answer 1

(a) (y^2/100)-(x^2/36)=1
(b) (x^2/100)-(y^2/36)=1
(c) (x^2/36)-(y^2/64)=1
(d) (y^2/36)-(x^2/64)=1

Answer 2

the other focus is at (0,10) i tihnk?

Answer 3

it says -10

Answer 4

well (0,-10)

Answer 5

by the location of the vertices, I think we can tell that the equation is of the form \(y^2/a^2−x^2/b^2=1\)

Answer 6

because

Answer 7

okay...

Answer 8

i get it so far

Answer 9

now we have to decide if it's a) or d).
hm, we'll do it without working too much. We know that the point (0,6) must be on the curve. So that means that the equation must be verified if you replace \(x\) by 0 and \(y\) by 6.