Question

If $x + y = k$is a normal to the parabola $y^{2} = 12x,$ then k is

• A. 3
• B. 9
• C. –9
• D. –3

Answer 1

Answer: (B)

9

Answer 2

Any normal to the parabola $y^{2} = 12x$is $y + tx = 6t + 3t^{3}$. It is identical with $x + y = k$if $\frac{t}{1} = \frac{1}{1} = \frac{6t + 3t^{3}}{k}$

∴$t = 1$and $1 = \frac{6 + 3}{k}$⇒$k = 9$