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If the line x-1=0 is the directrix of th...

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 `1/8` (b) 8 (c) 4 (d) `1/4`

Text Solution

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The correct Answer is:
C
Given, `y^(2) - kx - 8`
`implies y^(2) = k (x - (8)/(k))`
Shifing the origin `Y^(2) = hX`, 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
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