What is the directrix y^2+4x-14y=-53 ?

The directrix y^2+4x-14y=-53 is x=0

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directrix y^2+4x-14y=-53

directrix

y^{2} + 4 x - 14 y = - 53

x = 0

Solution steps

Rewrite

y^{2} + 4 x - 14 y = - 53

in the standard form

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

(h, k) = (- 1, 7), p = - 1

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

(- 1, 7)

x-coordinate

x = - 1 - p

x = - 1 - (- 1)

Refine

x = 0

y = 6 x^{2} + 12 x

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

4 X^{2} + 12 X + 9

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

y^{2} - 4 y - 8 x - 12 = 0