The circle has R radius and and ellipse is intersecting the circle. I need to findout $x_c$ and $y_c$, which is the midpoint of the 2 intersected point of ellipse.Line 3 is the tangent of the ellipsoid which passes through the farthest point on ellipse.
The equation of line 1:
$$\frac{x-x_c}{x_c-0}=\frac{y-y_c}{y_c-0}\quad;\qquad y-y_c=\frac{y_c}{x_c}(x-x_c)$$
Perpendicular of line 1 is line 2, equation of line 2:
$$y-y_c=-\frac{y_c}{x_c}(x-x_c)$$
the equation of line 3:
$$ax+by+c=0$$
and parallel to this line and passing through the point $(x_c,y_c)$ is line 4. The equation of line 4:
$$y-y_c=-\frac ab(x-x_c)$$
I do not know the value of $x_c$ and $y_c$. How to find out these unknowns ($x_c$ and $y_c$).Are those equations correct? Any help will be appreciated.
