The focus of the parabola {x^2} = 2x + 2y is | vedclass

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(C) The given equation of the parabola is ${x^2} = 2x + 2y$.Rearranging the terms,we get ${x^2} - 2x = 2y$.Completing the square on the left side: ${x

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$(1, 0)$

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(C) The given equation of the parabola is ${x^2} = 2x + 2y$.Rearranging the terms,we get ${x^2} - 2x = 2y$.Completing the square on the left side: ${x^2} - 2x + 1 = 2y + 1$.This simplifies to ${(x - 1)^2} = 2\left( y + \frac{1}{2} \right)$.Comparing this with the standard form ${(x - h)^2} = 4a(y - k)$,we have $4a = 2$,which gives $a = \frac{1}{2}$.The vertex $(h, k)$ is $(1, -\frac{1}{2})$.The focus of the parabola is given by $(h, k + a)$.Substituting the values,we get $(1, -\frac{1}{2} + \frac{1}{2}) = (1, 0)$.

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

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