What is the directrix 5x-x^2 ?

The directrix 5x-x^2 is y= 13/2

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directrix 5x-x^2

directrix

5 x - x^{2}

y = \frac{13}{2}

Solution steps

Rewrite

y = 5 x - x^{2}

in the standard form

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

(h, k) = (\frac{5}{2}, \frac{25}{4}), 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

(\frac{5}{2}, \frac{25}{4})

y-coordinate

y = \frac{25}{4} - p

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

Refine

y = \frac{13}{2}

y^{2} - 12 x - 12 y + 84 = 0

4 x^{2} + 10 x - 10

(x - 7)^{2} = - 12 (y - 1)

y^{2} = 5 y + 7 x + 3

2 y^{2} - 12 y - x + 5 = 0