The focus of the parabola y^2 - x - 2y + 2 = | vedclass

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(D) Given equation of the parabola is $y^2 - x - 2y + 2 = 0$.Rearranging the terms,we get $y^2 - 2y = x - 2$.Completing the square on the left side: $

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$(5/4, 1)$

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(D) Given equation of the parabola is $y^2 - x - 2y + 2 = 0$.Rearranging the terms,we get $y^2 - 2y = x - 2$.Completing the square on the left side: $(y - 1)^2 - 1 = x - 2$.$(y - 1)^2 = x - 1$.Let $Y = y - 1$ and $X = x - 1$. The equation becomes $Y^2 = X$.Comparing this with the standard form $Y^2 = 4aX$,we have $4a = 1$,so $a = 1/4$.The focus of $Y^2 = 4aX$ is $(a, 0)$,which is $(1/4, 0)$.To find the focus in the $(x, y)$ coordinate system,we substitute back:$X = 1/4 \implies x - 1 = 1/4 \implies x = 5/4$.$Y = 0 \implies y - 1 = 0 \implies y = 1$.Thus,the focus is $(5/4, 1)$.

The focus of the parabola $y^2 - x - 2y + 2 = 0$ is

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