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Maths-

General

Easy

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 -

– 6
6
$\frac{1}{4}$
– $\frac{1}{4}$

The correct answer is: – 6

The parabola is y² = k $open parentheses x – fraction numerator 6 over denominator K end fraction close parentheses$ &
Dirctrix x – $fraction numerator 6 over denominator K end fraction$ = $– fraction numerator K over denominator 4 end fraction$ $rightwards double arrow$ x = $fraction numerator 6 over denominator K end fraction$ $– fraction numerator K over denominator 4 end fraction$
Which coincides with line x = ½
$rightwards double arrow$ $fraction numerator 6 over denominator K end fraction$ – $fraction numerator K over denominator 4 end fraction$ = $fraction numerator 1 over denominator 2 end fraction$ $rightwards double arrow$ K² + 2K – 24 = 0
$rightwards double arrow$ (K + 6) (K – 4) = 0 $rightwards double arrow$ K = – 6, K = 4

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