What is the directrix 2y^2-16y+72=20x ?

The directrix 2y^2-16y+72=20x is x=-1/2

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directrix 2y^2-16y+72=20x

directrix

2 y^{2} - 16 y + 72 = 20 x

x = - \frac{1}{2}

Solution steps

Rewrite

2 y^{2} - 16 y + 72 = 20 x

in the standard form

4 \cdot \frac{5}{2} (x - 2) = (y - 4)^{2}

(h, k) = (2, 4), p = \frac{5}{2}

Parabola is symmetric around the x-axis and so the directrix is a line parallel to the y-axis, a distance

- p

from the center

(2, 4)

x-coordinate

x = 2 - p

x = 2 - \frac{5}{2}

Refine

x = - \frac{1}{2}

\frac{1}{2} x^{2}

4 y^{2} - 3 x = 0

y^{2} + 8 x - 4 y + 20 = 0

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

- 30 x^{2} + 28 x - 6