The length of the intercept cut by the line 4 x + 4 3 y - 1 = 0 between the curve y 2 = x is equal to

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Question: Answered & Verified by Expert

The length of the intercept cut by the line

4 x + 4 \sqrt{3} y - 1 = 0

between the curve

y^{2} = x

is equal to

MathematicsParabolaJEE Main

Options:

A $4$
B $9$
C $12$
D $16$

Solution:

1084 Upvotes Verified Answer

The correct answer is:

4

Given line is a focal chord for the parabola and its slope is

\tan α = \frac{- 1}{\sqrt{3}}

∴

Length of the focal chord

= 4 a {cosec}^{2} α = 4 \cdot \frac{1}{4} \cdot {(2)}^{2} = 4

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