The equation of the normal drawn to the parabola $y^2=6 x$ at the point $(24,12)$ is

The equation of the normal drawn to the parabola $y^2=6 x$ at the point $(24,12)$ is
  1. $3 x-y=60$
  2. $4 x+y=108$
  3. $2 x+y=60$
  4. $x-2 y=0$

Solution

$\begin{aligned} & \text { } y^2=6 x, \mathrm{P}(24,12) \\ & \Rightarrow 2 a=3 \end{aligned}$
Equation of normal in point form is $\begin{aligned} & y-y_1=\frac{-y_1}{2 a}\left(x-x_1\right) \Rightarrow y-12=\frac{-12}{3}(x-24) \\ & \Rightarrow 4 x+y=108 \end{aligned}$

Asked in: AP EAMCET 2024 (21 May Shift 1)

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