What is the directrix y=x^2-10x+5 ?

The directrix y=x^2-10x+5 is y=-81/4

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directrix y=x^2-10x+5

directrix

y = x^{2} - 10 x + 5

y = - \frac{81}{4}

Solution steps

Rewrite

y = x^{2} - 10 x + 5

in the standard form

4 \cdot \frac{1}{4} (y - (- 20)) = (x - 5)^{2}

(h, k) = (5, - 20), 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, - 20)

y-coordinate

y = - 20 - p

y = - 20 - \frac{1}{4}

Refine

y = - \frac{81}{4}

y = x^{2} - 6 x + 9

x^{2} - 2 x + 8 y + 9 = 0

\frac{1}{20} x^{2}

+ t^{2}

y^{2} - 4 x = 0