If P is a point on the line x + 4a = 0 and QR is the chord of contact of P with respect to y2 = 4ax, then ∠QOR (where O is the vertex) is equal to
(A) 45°
(B) 60°
(C) 30°
(D) 90°
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If P is a point on the line x + 4a = 0 and QR is the chord of contact of P with respect to y2 = 4ax, then ∠QOR (where O is the vertex) is equal to
(A) 45°
(B) 60°
(C) 30°
(D) 90°
If P is a point on the line x + 4a = 0 and QR is the chord of contact of P with respect to y2 = 4ax, then ∠QOR (where O is the vertex) is equal to
(A) 45°
(B) 60°
(C) 30°
(D) 90°
Correct option (D) 90°
Explanation
Let P be (x1, y1) so that
x1 + 4a = 0 …..(1)
Chord of contact of P(x1,y1) is
yy1 – 2a(x + x1) = 0
⇒ yy1 – 2ax + 8a2 = 0
[∴ x1 = -4a from Eq.(1)]
⇒ yy1 – 2a(x + x1) = 0
⇒ yy1 -2ax + 8a2 = 0
⇒ 2ax – y1y/8a2 = 1
Hence, the combined equation of the pair of lines OQ and OR is
y2 – 4ax(2ax – y1y/8a2)
In this equation, the coefficient of x2 + the coefficient of y2 = −1 + 1 = 0. Hence ∠QOR = 90°