NTA Abhyas JEE Main2020MathematicsParabolaPractice

The length of the normal chord which subtends an angle of 9 0 o at the vertex of the parabola y 2 = 4 x is

Options

A6 3 units
B7 2 units
C8 2 units
D9 2 units

Correct answer

A. 6 3 units

Step-by-step solution

For the normal chord, t 2 = - t 1 - 2 t 1 … 1 Also, the chord subtends an angle of 9 0 o at the vertex ∴ t 1 t 2 = - 4 … 2 From 1 , t 1 t 2 = - t 1 2 - 2 or - 4 = t 1 2 - 2 ∴ t 1 2 = 2 ∴ t 2 = - 4 t 1 = - 4 2 = - 2 2 or t 2 2 = 8 Now, P Q 2 = a 2 t 1 2 - t 2 2 2 + 4 a 2 t 1 - t 2 2 = 1 ⋅ 2 - 8 2 + 4 2 + 2 2 2 = 36 + 72 P Q 2 = 108 or P Q = 6 3 units

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