If P ( h , k ) be a point on the parabola x=4 y2, which is nearest to the point Q (0,33), then the distance of P from the directrix of the parabola y2=4(x+y) is equal to :

Question

If P ( h , k ) be a point on the parabola x=4 y2, which is nearest to the point Q (0,33), then the distance of P from the directrix of the parabola y2=4(x+y) is equal to : (A) 4 (B) 2 (C) 8 (D) 6

Tardigrade Admin · Accepted Answer

Equation of normal y=-t x+2 a t+a t3 y=-t x+(2/16) t+(1/16) t3 It passes through (0,33) 33=(t/8)+(t3/16) t 3+2 t -528=0 ( t -8)( t 2+8 t +66)=0 t =8 P ( at 2, 2 at )=((1/16) × 64,2 × (1/16) × 8)=(4,1) Parabola: y2=4(x+y) ⇒ y2-4 y=4 x ⇒(y-2)2=4(x+1) Equation of directix :- x+1=-1 x=-2 Distance of point =6 Ans.: (4)

Q. If P(h,k) be a point on the parabola x=4y2, which is nearest to the point Q(0,33), then the distance of P from the directrix of the parabola y2=4(x+y) is equal to :

4

2

8

6

Q. If $P (h, k)$ be a point on the parabola $x = 4 y^{2}$ , which is nearest to the point $Q (0, 33)$ , then the distance of $P$ from the directrix of the parabola $y^{2} = 4 (x + y)$ is equal to :