Question

If the line x - 1 = 0 is the directrix of the parabola y² - kx + 8 = 0, then one of the values of k is

(a)  1/8

(b)  8

(c)  4

(d)  1/4

Answer 1

Correct option (C) 4

Explanation :

The given parabola equation can be written as

where

X = x - 8/k and Y = y

Therefore

Y² = kX = 4(k/4)X

so that a = k/4. The equation of the directrix is

X + a = 0 ⇒ x-(8/k - k/4) = 0

Now x – 1 = 0 is the directrix. This implies

8/k - k/4 = 1

Therefore, one of the values of k is 4.