What is the directrix x^2-26x+65 ?

The directrix x^2-26x+65 is y=-417/4

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directrix x^2-26x+65

directrix

x^{2} - 26 x + 65

y = - \frac{417}{4}

Solution steps

Rewrite

y = x^{2} - 26 x + 65

in the standard form

4 \cdot \frac{1}{4} (y - (- 104)) = (x - 13)^{2}

(h, k) = (13, - 104), 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

(13, - 104)

y-coordinate

y = - 104 - p

y = - 104 - \frac{1}{4}

Refine

y = - \frac{417}{4}

y^{2} + 2 y + 1 = - 2 x + 4

y^{2} - 4 x + 4 y - 4 = 0

y = x^{2} - 6 x + 5

2 x^{2} - 19 x + 9

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