Question

If the line 2x – 1 = 0 is the derectrix of the parabola

y² – kx + 6 = 0 then one of the value of K is –

• A. – 6
• B. 6
• C. $\frac{1}{4}$
• D. – $\frac{1}{4}$

Answer 1

Answer: (A)

– 6

Answer 2

The parabola is y² = k $\left( x–\frac{6}{K} \right)$ &

Directrix x – $\frac{6}{K}$ = $–\frac{K}{4}$̃ x = $\frac{6}{K}$ $–\frac{K}{4}$

Which coincides with line x = ½

̃ $\frac{6}{K}$ – $\frac{K}{4}$ = $\frac{1}{2}$̃ K² + 2K – 24 = 0

̃ (K + 6) (K – 4) = 0 ̃ K = – 6, K = 4