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Question: Answered & Verified by Expert
If the line $y=2 x+k$ is normal to the parabola $y^2=4 x$, then $k=$
MathematicsParabolaAP EAMCETAP EAMCET 2020 (22 Sep Shift 1)
Options:
  • A -10
  • B 10
  • C 12
  • D –12
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.

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