Coordinates of foucs of the parabola $x^{2} - 2 a x + 2 a y = 0$ will be

(0, a)

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(a, 0)

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(0, - a)

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(- a, 0)

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Solution

The correct option is B $(a, 0)$
$x^{2} - 2 a x + 2 a y = 0$
$x^{2} - 2 a x = - 2 a y$
Adding $a^{2}$ both side
$x^{2} - 2 a x + a^{2} = - 2 a y + a^{2}$
$(x - a)^{2} = - 2 a (y - \frac{a}{2}) . . . . . . (1)$
Comparing equation (1) with the standard equation of parabola we get,
$x^{2} = 4 a y$
$x = 0, y = a = \frac{- a}{2}$
$x - a = 0$
$x = a$
$y - \frac{a}{2} = - \frac{a}{2}$
$y = 0$
Coordinate of focus of the parabola are $(a, 0)$

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