Problems Involving Conic Sections

Question

1.   Find the standard equation of the hyperbola whose conjugate axis is on the directrix of the parabola y² -5x+12y=-16, having the focus of the parabola as one of its foci, and the vertex of the parabola as one of its vertices. 

2.   Find the standard equation of the parabola opening to the left whose axis contains the major axis of the ellipse 4x² +9y² =144, whose focus is the center of the ellipse, and which passes through the co-vertices of this ellipse.

3.   Find the standard equation of the ellipse whose major and minor axes are the transverse and conjugate axes (not necessarily in that order) of the hyperbola y² -x²-4x-4y-4=0

Answer 1

desmos.com/calculator/jlqxu6usaz

Here is a Desmos graph for the parabola in part 2:

desmos.com/calculator/0eoj9huuti

Graph for part 3:

desmos.com/calculator/r8xnxnemlh