What is the directrix x=-4(y-7)^2+7 ?

The directrix x=-4(y-7)^2+7 is x= 113/16

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directrix x=-4(y-7)^2+7

directrix

x = - 4 (y - 7)^{2} + 7

x = \frac{113}{16}

Solution steps

Rewrite

x = - 4 (y - 7)^{2} + 7

in the standard form:

4 (- \frac{1}{16}) (x - 7) = (y - 7)^{2}

(h, k) = (7, 7), p = - \frac{1}{16}

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

(7, 7)

x-coordinate

x = 7 - p

x = 7 - (- \frac{1}{16})

Refine

x = \frac{113}{16}

2 y^{2} - 16 x = 0

(x + 2)^{2} - 4

y = \frac{1}{4} (x + 5)^{2} - 1

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

y = - 0.5 x^{2} - 3