What is the directrix 2x^2-12x+14-14y=0 ?

The directrix 2x^2-12x+14-14y=0 is y=-57/28

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directrix 2x^2-12x+14-14y=0

directrix

2 x^{2} - 12 x + 14 - 14 y = 0

y = - \frac{57}{28}

Solution steps

Rewrite

2 x^{2} - 12 x + 14 - 14 y = 0

in the standard form

4 \cdot \frac{7}{4} (y - (- \frac{2}{7})) = (x - 3)^{2}

(h, k) = (3, - \frac{2}{7}), p = \frac{7}{4}

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

(3, - \frac{2}{7})

y-coordinate

y = - \frac{2}{7} - p

y = - \frac{2}{7} - \frac{7}{4}

Refine

y = - \frac{57}{28}

(4 - x)^{2}

y = 7 x^{2}

x = (\frac{4}{5} - 3 y) \cdot (\frac{4}{5} + 3 y)

y = (6 x - 1) (3 x - 2)

y = \frac{x ^{2}}{32}

What is the directrix 2x^2-12x+14-14y=0 ?
The directrix 2x^2-12x+14-14y=0 is y=-57/28