AOB, COD are two unequal line segments bisecting at right angles. Then locus of a point P such that PA*PB=PC*PD is a
A) Circle
B) Parabola
C) Ellipse
D) Hyperbola
(Please explain)

Try drawing a sketch and see if you can figure it out. Hint: make AB>CD, and figure out if there are any points along AB that would satisfy the condition. Note that if P is at the origin PA*PB > PC*PD, and if P is at either A or B then PA*PB = 0 <PC*PD.