find h in the ellipse if
where a, b are the axes of the ellipse.
I agree with mr.fantastic, but let then you have a hyperbola. You know the equation of a hyperbola in general:
Now, for :
Consider the given equation:
(because h>0, we may divide the sides by h and also -h)
Now we have the standard equation of the hyperbola and that means you can determine and .
If the "-" was simply 'misplaced' and the equation was , then we can rewrite it as
and, dividing by h, which, for h> 0, is an ellipse. Assuming that "a" is the length of the semi-axis along the x-axis and "b" the length of the sem-axis along the y-axis, we have and .
From the first equation and from the second . so .