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)
$\therefore \:\: k = 4 + 8 = 12$