Question

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

y² – kx + 6 = 0 then one of the values of k is :

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

Answer 1

Answer: (A)

– 6

Answer 2

y² – kx + 6

y² = kx – 6

y² = k$\left( x–\frac{6}{k} \right)$

Directrix

x – $\frac{6}{k}$ = – $\frac{k}{4}$

x = $\frac{6}{k}$ – $\frac{k}{4}$ .......(i)

But directrix is given

x = $\frac{1}{2}$ .......... (ii)

comparing

$\frac{6}{k}$ – $\frac{k}{4}$ =$\frac{1}{2}$

̃ $\frac{24–k^{2}}{4k}$ = $\frac{1}{2}$

̃ 24 – k² = 2k

̃ k² + 2k – 24 = 0

̃ (k + 6)(k – 4) = 0

̃ k = – 6, k = 4