What is the directrix y^2+14y+4x+45=0 ?

The directrix y^2+14y+4x+45=0 is x=2

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directrix y^2+14y+4x+45=0

directrix

y^{2} + 14 y + 4 x + 45 = 0

x = 2

Solution steps

Rewrite

y^{2} + 14 y + 4 x + 45 = 0

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 = 2

2 x^{2} + x - 3

y = x^{2} - 8 x + 7

y = \frac{x ( x + 5 )}{7}

x^{2} + 9 x + 20

y = - 7 x^{2} - 3