What is the directrix y=-x^2+10x ?

The directrix y=-x^2+10x is y= 101/4

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directrix y=-x^2+10x

directrix

y = - x^{2} + 10 x

y = \frac{101}{4}

Solution steps

Rewrite

y = - x^{2} + 10 x

in the standard form

4 (- \frac{1}{4}) (y - 25) = (x - 5)^{2}

(h, k) = (5, 25), p = - \frac{1}{4}

Parabola is symmetric around the y-axis and so the directrix is a line parallel to the x-axis, a distance

- p

from the center

(5, 25)

y-coordinate

y = 25 - p

y = 25 - (- \frac{1}{4})

Refine

y = \frac{101}{4}

y = x^{2} + 3

y = x^{2} + 1

y = x^{2} + x - 1

4 x^{2} - 8 x - 3 y - 2 = 0

0 = (y - 1)^{2} - 16 (x + 4)