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Q.
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
NTA AbhyasNTA Abhyas 2020Conic Sections
Solution:
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