First slide

Parabola

Question

Let $L$ be a normal to the parabola $y^{2} = 4 x .$ If $L$ passes through the point $(9, 6)$ , then $L$ is not given by

Moderate

A

$y - x + 3 = 0$
B

$y + 3 x - 33 = 0$
C

$y + x - 15 = 0$
D

$y - 2 x + 12 = 0$

Solution

The equation of the normal is
$y = m x - 2 m - m^{3}$
As it passes through $(9, 6)$
$6 = 9 m - 2 m - m^{3} \Rightarrow m^{3} - 7 m + 6 = 0$
$\Rightarrow m = 1, 2, - 3$
Showing that $L$ is not given by (c).

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