What is the directrix 4x^2-8x+2y=5 ?

The directrix 4x^2-8x+2y=5 is y= 37/8

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directrix 4x^2-8x+2y=5

directrix

4 x^{2} - 8 x + 2 y = 5

y = \frac{37}{8}

Solution steps

Rewrite

4 x^{2} - 8 x + 2 y = 5

in the standard form

4 (- \frac{1}{8}) (y - \frac{9}{2}) = (x - 1)^{2}

(h, k) = (1, \frac{9}{2}), 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

(1, \frac{9}{2})

y-coordinate

y = \frac{9}{2} - p

y = \frac{9}{2} - (- \frac{1}{8})

Refine

y = \frac{37}{8}

88 x - 16 x^{2} - 112

- 16 t^{2} + 60 t + 3

\frac{x ^{2} - 4 x - 4}{2}

y = \frac{x ^{4} - x ^{2} - 2 x - 1}{x ^{2} - x - 1}

y = 6 x^{2}