What is the directrix 10x^2 ?

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directrix 10x^2

directrix

10 x^{2}

y = - \frac{1}{40}

Solution steps

Rewrite

y = 10 x^{2}

in the standard form:

4 \cdot \frac{1}{40} (y - 0) = (x - 0)^{2}

(h, k) = (0, 0), p = \frac{1}{40}

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

(0, 0)

y-coordinate

y = 0 - p

y = 0 - \frac{1}{40}

Refine

y = - \frac{1}{40}

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

(x + 5)^{2} = 12 (y - 2)

y^{2} + 4 x - 80 y + 20 = 0

- x^{2} - 4 x + 1

y - 7 = \frac{1}{24} (x + 4)^{2}