Question 1204749
<pre>
{{{drawing(400,200,-10,1.8,-4,2, grid(1),
triangle(2,4,2,-5,2,-6), triangle(-11,2,3,2,4,2),
graph(400,200,-10,1.8,-4,2, (1/6)(sqrt(x^2+8x+7)-9)),
graph(400,200,-10,1.8,-4,2, (1/6)(-sqrt(x^2+8x+7)-9)),
circle(-4,-3/2,.08),
blue(line(-7,-3/2,-1,-3/2),line(-4,-1,-4,-2),line(-4.04,-1,-4.04,-1),line(-4+.04,-1,-4+.04,-1)),
green(line(-7,-1,-1,-1),line(-7,-2,-1,-2),line(-7,-1,-7,-2),line(-1,-1,-1,-2)) 




)}}}

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

The horizontal blue line I added:
The transverse axis extends from vertex (-7,-3/2) to vertex (-1,-3/2)
so the transverse axis is 6 units long. The semi-transverse axis is
'a' which is half of 6 or a=3.

The vertical blue line that I added:
The conjugate axis extends from midpoint of top side to midpoint of 
bottom side of defining rectangle, from (4,-1) to vertex (-4,-2)
so the conjugate axis is 1 units long. The semi-conjugate axis is
'b' which is half of 1 or b=1/2.

The center is (h,k)=(-4,-3/2) so the equation becomes in standard form

{{{(x+4)^2/3^2-(y+3/2)^2/(1/2)^2=1}}}

Now if you do some work on that, you'll 

end up with this general form: 

{{{x^2 - 36 y^2 + 8x - 108y - 74 = 0}}}

Edwin</pre>