A ray emitting from the point $(-4,0)$ is incident on the ellipse $9x^2+25y^2=225$ at the point $P$ with abscissa $3$. Find the equation of the reflected ray after first reflection.
Points on the ellipse are $(3, \pm 12/5)$ and then equation of normal can be found at that point. After that we can find angle between reflected ray and normal and then find another line which is at same angle to normal but this approach is requiring too much too much calculation. Could someone suggest a better approach?
HINT...It is straightforward to calculate the eccentricity and to ascertain that $(-4,0)$ is one of the foci of the ellipse.
There is a standard theorem that says the normal to the ellipse bisects the focal radii, so the line you want to find joins the other focus $(4,0)$ to the point of contact on the ellipse.
I hope this helps.