Question

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. ¼

Answer 1

Answer: (C)

4

Answer 2

The parabola is y² = 4$\frac{k}{4}\left( x - \frac{8}{k} \right)$

Putting y = Y, x – 8/k = X, the equation is Y² = 4.$\frac{k}{4}$.X.

∴ The directrix is X + $\frac{k}{4}$ = 0 ie., x= $\frac{8}{k} + \frac{k}{4} = 0$

But x – 1 = 0 is the directrix. So, $\frac{8}{k} - \frac{k}{4} = 1 \Rightarrow k = - 8,4$