Show that the foot of the perpendicular drawn from the centre on any tangent to the ellipse lies on the curve
The equation of the tangent at any point is
Let be the foot of the perpendicular from the centre (0,0) to the
tangent,then Product of the slopes of PM and CM is -1.
. Equation 2.
Therefore, Equation 3.
But M lies on the first line.
Therefore, from 2,
Henc the P lies on