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

(1, 1)

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(1, 2)

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(2, 0)

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(2, 2)

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Solution

The correct option is C $(1, 2)$
The given parabola is $y^{2} - 4 y - 8 x - 4 = 0$
$\Rightarrow y^{2} - 4 y = 8 x + 4$
$\Rightarrow y^{2} - 4 y + 4 = 8 x + 4 + 4$
$\Rightarrow (y - 2)^{2} = 8 (x + 1)$
Comparing with standard parabola $Y^{2} = 4 a X$
We get, $X = x + 1, Y = y - 2, a = 2$
The focus of parabola is given by, $(X = a, Y = 0)$
i.e. $(x + 1 = 2, y - 2 = 0) = (x = 1, y = 2) = (1, 2)$
Hence option 'B' is correct choice

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