Question

find the equation of the hyperbola with foci at (-1,-10) and (-1,2) and vertices at (-1,-8) and (-1,0)


Can someone explain how to do this to me?

Answer 1

I'm just making a rough sketch, looks to me it's vertical, the centre is half way between the vertices, and since it's vertical we have the equation \[\frac{ (y-k)^2 }{ a^2 }-\frac{ (x-h)^2 }{ b^2 }=1\] where a is the transverse semi - axis (distance from center to vertex, the positive denominator) and b is the conjugate semi-axis (negative denominator)