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If the line $y=2 x+k$ is normal to the parabola $y^2=4 x$, then $k=$
Options:
Solution:
1194 Upvotes
Verified Answer
The correct answer is:
–12
Since, equation of normal to the parabola $y^2=4 a x$ having slope $m$ is $y=m x-2 a m-a m^3$.
So, equation of normal to the parabola $y^2=4 x$ is
$$
y=2 x+k
$$
Therefore,
$$
\begin{aligned}
k & =-2(1)(2)-(1)(2)^3 \\
& =-4-8=-12
\end{aligned}
$$
Hence, option (4) is correct.
So, equation of normal to the parabola $y^2=4 x$ is
$$
y=2 x+k
$$
Therefore,
$$
\begin{aligned}
k & =-2(1)(2)-(1)(2)^3 \\
& =-4-8=-12
\end{aligned}
$$
Hence, option (4) is correct.
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