Question

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

Answer 1

We have

y² = 12x = 4(3)x

which implies that every point on the parabola is of the form (3t ², 6t). The normal at (3t, 6t) is

tx + y = 6t + 3t³  ...(1)

However,

x + y = a    ..(2)

is the normal. That is, Eqs. (1) and (2) represent the same line. Therefore

t/1 = 1/1 = 6t + 3t³/a = t = 1 and a = 9