I'm trying to find the point where a line intersects a general ellipse centered at $(x_0,y_0)$, i.e $\frac{(x-x_0)^2}{a^2}+ \frac{(y-y_0)^2}{b^2} = 1$. The line is given by the points $(x_1,y_1)$ and $(x_0,y_0)$, i.e its a line from the center of the ellipse to a given point outside the ellipse. How to find the point on the ellipse where this line intersects this ellipse? I am a bit stumped.


This equation gives me the point i'm looking (xc,yc) for if the ellipse would be a circle:

x_c = xo + R*(x1-x0)/sqrt((x1-x0)^2+(y1-y0)^2)

and equivalently for y_c. I'm essentially trying to modify this equation to be for an ellipse.

Best regards MC

  • $\begingroup$ That’s not a “general” ellipse: it’s still axis-aligned. $\endgroup$
    – amd
    Jul 13, 2017 at 20:35

1 Answer 1



Substitute in the ellipse equation $y-y_0=m(x-x_0)$, where $m=(y_1-y_0)/(x_1-x_0)$, and solve for $x$.

  • $\begingroup$ Thank you my good sir! I seemed to have forgotten basic maths for a moment there $\endgroup$
    – Michel
    Jul 13, 2017 at 16:41

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.