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If the line $y=-x+k$ is normal to the curve $y^2=16 x$, then $k$ is
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Verified Answer
The correct answer is:
12
Normal of the parabola $y^2=16 x$ is
$$
y=m x-8 m-4 m^3
$$
Now, $y=-x+k$ is normal of parabola
$$
\therefore \quad m=-1
$$
put $m=-1$ in Eq. (i) we get
$$
\begin{aligned}
y & =-x+8+4 \\
y & =-x+12 \\
\therefore \quad k & =12
\end{aligned}
$$
$$
y=m x-8 m-4 m^3
$$
Now, $y=-x+k$ is normal of parabola
$$
\therefore \quad m=-1
$$
put $m=-1$ in Eq. (i) we get
$$
\begin{aligned}
y & =-x+8+4 \\
y & =-x+12 \\
\therefore \quad k & =12
\end{aligned}
$$
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