Correct Answer - Option 3 : 4
Concept:
The directrix of a parabola whose is equation is of the form (y - q)2 = 4a(x - p), is the line x = p - a.
Calculation:
The given equation of the parabola y2 = kx - 8 can be re-written as:
⇒ \(\rm (y-0)^2=4\left(\frac{k}{4}\right)\left(x-\frac{8}{k}\right)\)
Comparing the above equation with the general form of the equation (y - q)2 = 4a(x - p), we have:
q = 0, \(\rm a=\frac k4\), \(\rm p=\frac 8k\).
The equation of the directrix is:
x = p - a
⇒ \(\rm x=\frac 8k-\frac k4\)
According to the question, x = 1 is the directrix.
∴ \(\rm \frac 8k-\frac k4=1\)
⇒ k2 + 4k - 32 = 0
⇒ k2 + 8k - 4k - 32 = 0
⇒ k(k + 8) - 4(k + 8) = 0
⇒ (k + 8)(k - 4) = 0
⇒ k + 8 = 0 OR k - 4 = 0
⇒ k = -8 OR k = 4.