Question 1180954
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The transverse axis (between the two vertices) is horizontal, so the branches of the hyperbola open left and right; the general equation is<br>
{{{(x-h)^2/a^2-(y-k)^2/b^2=1}}}<br>
The center is halfway between the two vertices, at (7,9).<br>
a is the distance from the center to either vertex, so a=6; a^2=36.<br>
c is the distance from the center to either focus, so c=9; c^2=81.<br>
b^2=c^2-a^2=45<br>
ANSWER: {{{(x-7)^2/45-(y-9)^2/36=1}}}<br>