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Ellipse-Line Intersection


Ellipse-LineIntersection

The intersection of an ellipse centered at the origin and semiaxes of lengths a and b oriented along the Cartesian axes with a line passing through the origin and point (x_0,y_0) is given by simultaneously solving the equations

(x^2)/(a^2)+(y^2)/(b^2)=1
(1)
y=(y_0)/(x_0)x
(2)

for x and y, yielding the points

x=+/-(ab)/(sqrt(a^2y_0^2+b^2x_0^2))x_0
(3)
y=+/-(ab)/(sqrt(a^2y_0^2+b^2x_0^2))y_0.
(4)

See also

Circle-Line Intersection, Ellipse, Line

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Cite this as:

Weisstein, Eric W. "Ellipse-Line Intersection." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/Ellipse-LineIntersection.html

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