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

(0, 2)

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(1, 2)

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(4, 2)

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(1, 3)

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Solution

The correct option is A $(0, 2)$
$\Rightarrow y^{2} = 4 y - 4 x$
$\Rightarrow y^{2} - 4 y = - 4 x$
$\Rightarrow y^{2} - 4 y + 4 = - 4 x + y$
$\Rightarrow (y - 2)^{2} = - 4 (x - 1)$
vertex = $(1, 2)$
$\frac{1}{4 p} = \frac{- 1}{4} \to p = - 1$
$∴$ Focus = $(- 1 + 1, 2 + 0) = (0, 2)$

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