# Finding point on ellipse given center point and point outside the ellipse

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.

edit:

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

• That’s not a “general” ellipse: it’s still axis-aligned. – amd Jul 13 '17 at 20:35

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 $x$.