What is the directrix 4x^2-8x-3y-2=0 ?

The directrix 4x^2-8x-3y-2=0 is y=-35/16

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directrix 4x^2-8x-3y-2=0

directrix

4 x^{2} - 8 x - 3 y - 2 = 0

y = - \frac{35}{16}

Solution steps

Rewrite

4 x^{2} - 8 x - 3 y - 2 = 0

in the standard form

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

(h, k) = (1, - 2), p = \frac{3}{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

(1, - 2)

y-coordinate

y = - 2 - p

y = - 2 - \frac{3}{16}

Refine

y = - \frac{35}{16}

0 = (y - 1)^{2} - 16 (x + 4)

(x + 6)^{2} = 12 (y + 1)

- \frac{1}{8} (x - 8)^{2} + 2

y = 25 x^{2} - 36

- \frac{1}{2} x^{2} + 7 x - 3