How to write a system of equation that satisfies the conditions "a hyperbola and an ellipse that intersect in two points?"

Question

1308 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-05-04T02:10:34

Please see the explanation for 2 general examples.

A hyperbola with a horizontal transverse axis:

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

is tangent at its 2 vertices to the 2 ends of major axis of a parabola:

#(x-h)^2/a^2+(y-k)^2/b^2=1;a>b#

Where the values of a, h and k are the same for both equations.

A hyperbola with a vertical transverse axis:

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

is tangent at its 2 vertices to the 2 ends of major axis of a parabola:

#(y-k)^2/a^2+(x-h)^2/b^2=1;a>b#

Where the values of a, h, and k are the same for both equations.