Whats the length of chord intercepted by the parabola $y^{2} = 4 x o n t h e l i n e x + y = 0$

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Solution

The correct option is B

For this kind of question we usually solve the equations, find the points of intersection and then find the distance between these points. This distance would be equal to the intercept length given equation,

Parabola: $y^{2} = 4 x$

Line : $x + y = 0$

Solving these

$y^{2} = 4 x$

=-4y

$y^{2} + 4 y = 0$

$y (y + 4) = 0$

y=0 or -4

$∴ p o i n t s i n t e r s e c t i o n (0, 0) a n d (4, - 4)$

$∴ I n t e r s e p t l e n g t h \equiv \sqrt{4^{2} + 4^{2}} = \sqrt{32} = 4 \sqrt{2}$

Suggest Corrections

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