The equation {y^2} - 2x - 2y + 5 = 0 represen | vedclass

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Question

(C) Given equation: ${y^2} - 2x - 2y + 5 = 0$Rearranging the terms: ${y^2} - 2y = 2x - 5$Adding $1$ to both sides to complete the square: ${y^2} - 2y

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$A$ parabola whose directrix is $x = \frac{3}{2}$

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(C) Given equation: ${y^2} - 2x - 2y + 5 = 0$Rearranging the terms: ${y^2} - 2y = 2x - 5$Adding $1$ to both sides to complete the square: ${y^2} - 2y + 1 = 2x - 5 + 1$${(y - 1)^2} = 2x - 4$${(y - 1)^2} = 2(x - 2)$This is of the form ${(y - k)^2} = 4a(x - h)$,where $4a = 2$,so $a = \frac{1}{2}$,vertex $(h, k) = (2, 1)$.The focus is $(h + a, k) = (2 + \frac{1}{2}, 1) = (\frac{5}{2}, 1)$.The directrix is $x = h - a = 2 - \frac{1}{2} = \frac{3}{2}$.

The equation ${y^2} - 2x - 2y + 5 = 0$ represents:

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