Ellipse and locus of point of intersection of two tangents
Prove that the line lx+my+n=0 is a tangent to the ellipse if .
Tangents are drawn from a point P to the ellipse. Lines from the origin are drawn perpendicular to the tangents. If these lines are conjugate diameters, prove that the equation of the locus of P is
I have proved the first part.
For this next part the equation of a tangent to an ellipse in the form
gradients are related by
I used the two gradients, m, in two equations for tangents and tried to solve for x and y, am I doing it right? because I get very very long and difficult expressions.