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 equation of $L$
can not be

Moderate

A

$y - x + 3 = 0$
B

$y + 3 x - 33 = 0$
C

$y + x - 15 = 0$
D

$y - 2 x + 12 = 0$

Solution

Equation of a normal to the parabola $y^{2} = 4 x$ is
$y = m x - 2 m - m^{3}$ which passes through (9, 6) if
$\begin{array}{l} m^{3} - 7 m + 6 = 0 \\ \Rightarrow m = 1, 2, - 3 \end{array}$
So equation of $L$ can not be $y + x - 15 = 0$ .

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