Question

Let P and Q be points (4, –4) and (9, 6) on the parabola y² = 4a(x–b). R is a point on the parabola so that area ΔPRQ is maximum, then

(a)  ∠PRQ = 90°

(b)  the point R is (4,4)

(c)  the point R is(1/4,1)

(d)  None of these

Answer 1

Correct option  (b)  the point R is (4,4) 

Explanation:

 (4,– 4) lies on y² = 4a(x – b)

16 = 4a(4 – b) (9,6)

lies on y² = 4a(x – b)

36 = 4a(9 – b)

9/4 = 9 - b/4 - b

⇒ b = 0 , a = 1

 y² = 4x

Let R be (t² ,2t)

= –5(t² – t – 6) = – 5(t - 1/2)² + 30 + 5/4

Area is maximum when t = 1/2

Coordinates of R(1/4, 1)