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) of these

Answer 1

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

Explanation:

(4,– 4) **** on y2 = 4a(x – b)

16 = 4a(4 – b) (9,6)

**** 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)