Coordinates of the focus of the parabola $x^{2} - 4 x - 8 y - 4 = 0$ are

(0.2)

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(2,1)

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(1,2)

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(-2,-1)

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Solution

The correct option is B (2,1)
$x^{2} - 4 x = 8 y + 4$
$(x - 2)^{2} = 8 y + 4 + 4$
$(x - 2)^{2} = 8 (y + 1) = 4 \times 2 (y + 1)$
$(x - h)^{2} = 4 p (y - k)$
$h = 2, p = 2, k = - 1$
Coordinates of four : (h, k+p)
$\Rightarrow (2, - 1 + 2) \Rightarrow (2, 1)$

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