Let the point is P(h,k). By definition of parabola a. The locus of point P(h,k) which moves in a plane such that its distance from a fixed point (-2,3)S is always in a constant ratio to its perpendicular distance from a fixed straight line (x+6=0)M. i.e., ‌
PS
PM
=1‌‌(∵e=1 for parabola ) ⇒‌‌(PS)2=(PM)2 ⇒‌‌(h+2)2+(k−3)2=‌