# Identify an equation in standard form for a hyperbola with center (0, 0), vertex (0, 7), and focus (0, 11). ?

Jul 28, 2018

The equation of the hyperbola is ${y}^{2} / 49 - {x}^{2} / 72 = 1$

#### Explanation:

This is a hyperbola with a vertical transverse axis.

The general equation is

${\left(y - k\right)}^{2} / {a}^{2} - {\left(x - h\right)}^{2} / {b}^{2} = 1$

The center is $C = \left(h , k\right) = \left(0 , 0\right)$

As the foci are $F = \left(0 , 11\right)$ and $F ' = \left(0 , - 11\right)$

$c = 11$

As the vertices are $A = \left(0 , 7\right)$ and $A ' = \left(0 , - 7\right)$

$a = 7$

And

${b}^{2} = {c}^{2} - {a}^{2} = {11}^{2} - {7}^{2} = 121 - 49 = 72$

The equation of the hyperbola is

${y}^{2} / 49 - {x}^{2} / 72 = 1$

graph{(y^2/49-x^2/72-1)=0 [-60.26, 56.84, -20.9, 37.6]}