Question

The ends of a line segments are P (1, 3) and Q (1, 1). R is a point on the line segment PQ such that PR : QR = 1 : l. If R is an interior point of the parabola y² = 4x then –

• A. lÎ (0, 1)
• B. lÎ$\left( –\frac{3}{5},1 \right)$
• C. l Î$\left( \frac{1}{2},\frac{3}{5} \right)$
• D. None of these

Answer 1

Answer: (A)

lÎ (0, 1)

Answer 2

R = [1, 1+3l/1+l] It is an interior point of

y²– 4x =0

if [1+3l/1+l] – 4<0–3/5<l<1. But l > 0

\ l ฮ (0, 1)

For the parabola y² = 4ax a chord AB joining the points A (at₁², 2at₁) & B (at₂², 2at₂) is drawn. The equation of AB is given by.

y (t₁ + t₂) = 2x + 2at₁t₂