Question

The length of intercept cut by the line $4x+4\sqrt{3}y-1=0$ on the curve $y^2=4\left(x+\frac{3}{4}\right)$ is equal to

• A. $4$ units
• B. $9$ units
• C. $12$ units
• D. $16$ units

Answer 1

Answer: (D)

The given line passes through the focus $\left(\frac{1}{4},0\right)$ , so it is a focal chord for the given parabola.
Hence, its slope is $tan\alpha =\frac{-1}{\sqrt{3}}$
$\therefore$ the length of the intercept is the same as the length of the focal chord
Hence, the length of the intercept $=4a{\left(\text{cosec}\right)}^2\alpha =4\cdot 1\cdot {\left(2\right)}^2=16$ units