If the line $ x-1=0 $ is the directrix of the parabola $ y^{2}-k x+8=0 $, then one of the values of $ k $ is

Question

If the line $ x-1=0 $ is the directrix of the parabola $ y^{2}-k x+8=0 $, then one of the values of $ k $ is, $ \frac{1}{8} $, $ 8 $, $ \frac{1}{4} $, $ 4 $

MARKS App · Accepted Answer

Given, y 2 = k x - 8 ⇒ y 2 = k x - 8 k Shifting the origin Y 2 = k X where Y = y , X = x - 8 k Directrix of standard parabola is X = - k 4 Directrix of original parabola is x = 8 k - k 4 Now, x = 1 also coincides with x = 8 k - k 4 On solving, we get k = 4 , - 8

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