The Vertex of the parabola $y^{2} - 10 y + x + 22 = 0$ is.

(3,4)

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(3,5)

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(5,3)

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none of these

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Solution

The correct option is B (3,5)
Given,

$y^{2} - 10 y + x + 22 = 0$

$\Rightarrow x = - y^{2} + 10 y - 22$

$x = - {(y - 5)}^{2} + 3$

$x - 3 = - {(y - 5)}^{2}$

$- (x - 3) = {(y - 5)}^{2}$

$4 (- \frac{1}{4}) (x - 3) = {(y - 5)}^{2}$

$(h, k) = (3, 5), p = - \frac{1}{4}$

Vertex of parabola $(3, 5)$

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