Question

If $x+y=k$ is a normal to the parabola $y^2=16x$, then $k=$

• A. 3
• B. 9
• C. 12
• D. 15

Answer 1

Answer: (C)

We have, $y^2=16x$ ...(i)
Differentiating w.r.t. y, we get
$2y=16\frac{dx}{dy}\Rightarrow \frac{dx}{dy}=\frac{y}{8}$
Slope of normal $=-\frac{dx}{dy}=-\frac{y}{8}$
Now, $x+y=k$ .....(ii)
$\Rightarrow y=-x+k$
Slope = - 1
$\therefore -\frac{y}{8}=-1\Rightarrow y=8$
Substitutein (i), we get $x=4$
Now, put $x=4,y=8$ in (ii)
$\therefore k=4+8=12$