First slide

Parabola

Question

Equation of the normal at a point on the parabola
$y^{2} = 36 x$ , whose ordinate is three times its abcissac
is-

Moderate

A

$2 x + 3 y + 44 = 0$
B

$2 x - 3 y + 44 = 0$
C

$2 x + 3 y - 44 = 0$
D

$2 x - 3 y = 0$

Solution

Equation of the normal at $(9 m^{2}, - 18 m)$ on the
parabola is $y = m x - 2 \times 9 m - 9 m^{3}$ where $- 18 m = 3 \times 9 m^{2} .$
i.e., $m = 0 or m = - 2 / 3 . For m = - 2 / 3,$ the equation
of the normal is $2 x + 3 y - 44 = 0$ .

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