Ellipse-Line Intersection

Author

Eric W. Weisstein
February 10, 2009

This notebook downloaded from http://mathworld.wolfram.com/notebooks/PlaneGeometry/Ellipse-LineIntersection.nb.

For more information, see Eric's MathWorld entry http://mathworld.wolfram.com/Ellipse-LineIntersection.html.

©2009 Wolfram Research, Inc. except for portions noted otherwise

Solve

Solve[{((x^2)/(a^2))+((y^2)/(b^2))==1&&y==(y0/x0)x},{x,y}]

With[{pt=((a b )/(Sqrt[(b^2) (x0^2)+(a^2) (y0^2)])){x0,y0}},Manipulate[Graphics[{Circle[{0,0},{a,b}],Line[{-pt,{x0,y0}}],
PointSize[.02],Red,Point[{x0,y0}],
{Blue,Point[{-pt,pt}]}},Axes->True],{{a,1},0,1},{{b,.5},0,1},{{x0,-1},-1,1},{{y0,1},-1,1}]
]