Question 1103415
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The center, vertex, and focus have the same y value, so the branches of the hyperbola open to the right and left.  Then the equation in standard form is<br>
{{{(x-h)^2/a^2-(y-k)^2/b^2 = 1}}}<br>
With the equation in this form...
(1) the center is (h,k);
(2) the distance to each vertex is a; and
(3) the distance to each focus is c, where {{{c^2 = a^2+b^2}}}<br>
The center is given as (-3,5), so h=-3 and k=5.
The distance to each vertex is given as 2, so a=2.
The distance to each focus is given as 3, so c=3; that means b=sqrt(5).<br>
Plugging all these values into the standard form, we have the equation of the hyperbola:<br>
{{{(x+3)^2/4-(y-5)^2/5 = 1}}}<br>