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=
|h+6|2
(√(1)2)2
⇒h2+4+4h+k2+9−6k=(h+6)2 ⇒h2+k2+4h−6k+13=h2+36+12h
⇒k2−8h−6k−23=0 ∴ Required locus is y2−8x−6y−23=0