Question

If x + y = k is a normal to the parabola y² = 12x, then the value of k is

(A)  3

(B)  0

(C)  9 

(D)  3

Answer 1

Correct option  (C)  9 

Explanation :

We have y² = 12x = 4(3), x = 4ax where a = 3. Every point on the parabola is of the form (3t², 6t). Suppose x + y = k is normal at (3t ², 6t). Equation of the normal at (3t², 6t) is tx + y = 6t + 3t³. Therefore

t/1 = 1/1 = 6t + 3t³/k

t = 1 and k = 6 + 3 = 9