All conics can be expressed in polar form as:
, where the focus is at the origin.
A line that passes through the focus would intersect at points and
so
Can you show that this does not depend on ?
A straight line D through the focus F of a conic meets in two points A and B.
Show that the quantity
is independent of the choice of line D.
Not sure where to start with this one apart from maybe trying the 3 different conics of hyperbola, parabola and ellipse. Could someone give me a hint where to start?