Question 147644
Hello....I have just a couple of questions. Actually, two questions in one. 
What is the maximum number of intersections of the graphs of an ellipse and a parabola? 

{{{drawing(200,400,-5,5,-10,10,

graph(200,400,-5,5,-10,10, sqrt(40-6x^2)),
graph(200,400,-5,5,-10,10, 3x^2-9),
graph(200,400,-5,5,-10,10, -sqrt(40-6x^2)) )}}}

See, these cross in 4 points.

An ellipse and a hyperbola? 

{{{drawing(200,400,-5,5,-10,10,

graph(200,400,-5,5,-10,10, sqrt(-40+6x^2)),
graph(200,400,-5,5,-10,10,sqrt((64-4x^2)/16)),
graph(200,400,-5,5,-10,10, -sqrt(-40+6x^2) ),
graph(200,400,-5,5,-10,10,-sqrt((64-4x^2)/16)) )}}}

Also 4.

Thank you very much!

You're welcome.

Edwin