What is the directrix y=(5x-8)^2 ?

The directrix y=(5x-8)^2 is y=-1/100

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directrix y=(5x-8)^2

directrix

y = (5 x - 8)^{2}

y = - \frac{1}{100}

Solution steps

Rewrite

y = (5 x - 8)^{2}

in the standard form:

4 \cdot \frac{1}{100} (y - 0) = (x - \frac{8}{5})^{2}

(h, k) = (\frac{8}{5}, 0), p = \frac{1}{100}

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{8}{5}, 0)

y-coordinate

y = 0 - p

y = 0 - \frac{1}{100}

Refine

y = - \frac{1}{100}

y = 5 x^{2} + 6 x - 7

(x - 1)^{2} = - 6 (y + 4)

7 x^{2} + 70 x + 178

x^{2} - 6 x - 28 y = - 93

x^{2} + 17 x + 16