What is the directrix 3-4x^2 ?

The directrix 3-4x^2 is y= 49/16

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directrix 3-4x^2

directrix

3 - 4 x^{2}

y = \frac{49}{16}

Solution steps

Rewrite

y = 3 - 4 x^{2}

in the standard form:

4 (- \frac{1}{16}) (y - 3) = (x - 0)^{2}

(h, k) = (0, 3), p = - \frac{1}{16}

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)

y-coordinate

y = 3 - p

y = 3 - (- \frac{1}{16})

Refine

y = \frac{49}{16}

2 y^{2} - 5 y + x - 4 = 0

x^{2} + 2 x - 8

x^{2} + 2 x - 1

y^{2} - 16 x = 0

2 x^{2} - 8 x + 9