KEAM 2013 Math Paper

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

⇒‌‌k2−8h−6k−23=0
∴ Required locus is
y2−8x−6y−23=0