Let ABCD be a quadrilateral. Suppose there exists a parabola WA with focus A, tangent to lines BC, CD, and DB, and a parabola WC with focus C tangent to lines AB, BD, and AD.
Suppose that WAand WC are tangent to line BD at X and Y respectively. Prove that BX = DY.
I wish to solve the above problem using coordinate geometry
For the sake of simplicity we can assume either one parabola to be y² = 4ax, right? Could someone tell me how to proceed, and possibly post a detailed solution for the same?
I think proving BX = DY can possibly be done using pure geometry/congruence, but, as a student of analytic geometry I wish to proceed using the cartesian coordinate system.
Thanks a lot!