Question

If the line \( x - 1 = 0 \) is the directrix of the parabola \( y^2 - kx + 8 = 0 \), then one of the values of \( k \) is

• A. \( \frac{1}{8} \)
• B. 8
• C. 4
• D. \( \frac{1}{4} \)

Hint:

For problems involving parabolas and their directrices, use the properties of the vertex form and directrix-focus relation to find the unknown constants.

Answer 1

The Correct Option is C

The equation of the parabola \( y^2 = kx - 8 \) implies that the directrix is at \( x = 1 \). Solving for \( k \) using the geometric properties of the parabola, we find \( k = 4 \).