Question

The ends of a line segment are P(1, 3) & 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. l Î$\left( - \frac{3}{5},1 \right)$
• 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 = $\left( 1,\frac{1 + 3\lambda}{1 + \lambda} \right)$

It is an interior point of y² – 4x = 0 then

$\left( \frac{1 + 3\lambda}{1 + \lambda} \right)^{2}$– 4 (1) < 0

\ –$\frac { 3 } { 5 }$ < l < 1

But l > 0, \ l Î (0, 1)