How to write a system of equation that satisfies the conditions "a circle and an ellipse that do not intersect?"
1 Answer
Explanation:
The equation of a circle with centre
#(x-h)^2 + (y-k)^2 = r^2#
The equation of an ellipse with horizontal and vertical axes, centre
#(x-h)^2/a^2+(y-k)^2/b^2 = 1#
Perhaps the simplest example of a non-intersecting system would involve a concentric circle and ellipse with the smaller semi axis larger than the radius of the circle.
So we could write:
#{ (x^2+y^2 = 1), (x^2/4+y^2/9=1) :}#
graph{(x^2+y^2-1)(x^2/4+y^2/9-1) = 0 [-10, 10, -5, 5]}
The largest possible finite number of intersections between a circle and an ellipse is
#{ (x^2+y^2 = 4), (x^2+y^2/9=1) :}#
graph{(x^2+y^2-4)(x^2+y^2/9-1) = 0 [-10, 10, -5, 5]}