What is the directrix y=2x^2+3pi ?

The directrix y=2x^2+3pi is y=3pi-1/8

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directrix y=2x^2+3pi

directrix

y = 2 x^{2} + 3 π

y = 3 π - \frac{1}{8}

Solution steps

Rewrite

y = 2 x^{2} + 3 π

in the standard form:

4 \cdot \frac{1}{8} (y - 3 π) = (x - 0)^{2}

(h, k) = (0, 3 π), p = \frac{1}{8}

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, 3 π)

y-coordinate

y = 3 π - p

y = 3 π - \frac{1}{8}

x = (2 y - 1) (5 y - 6)

+ 2 (x + 1)^{2} - 3

x^{2} - 6 y = 0

- 8 (y - 3) = (x + 4)^{2}

y = x^{2} - 10 x + 25