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

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Answer 1 · 2018-07-28T12:17:39

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

This is a hyperbola with a vertical transverse axis.

The general equation is

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

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

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

$c=11$

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

$a=7$

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]}