Question

R is a point inside the parabola y² = 4x and it divide the line segment PQ internally in l : 1. If P is (1, 3) and Q is (1, 1), then the range of l is

• A. (1, )
• B. (– , –5/3) Č (1, )
• C. (5/3, )
• D. (–5/3, 1)

Answer 1

Answer: (A)

(1, )

Answer 2

R $\left( 1 , \frac { 3 + \lambda } { \lambda + 1 } \right)$ d₁ < 0 Ž $\left( \frac { 3 + \lambda } { \lambda + 1 } \right) ^ { 2 }$– 4 < 0

Ž l² + 6l + 9 – 4l² – 8l – 4 < 0 (l ¹ –1)

Ž 3l² + 2l – 5 > 0

Ž (3l + 5) (l – 1) > 0

Ž l Ī (– , –5/3) Č (1, )

but l > 0 \ l > 1