What is the directrix y^2+6y-2x+13=0 ?

The directrix y^2+6y-2x+13=0 is x= 3/2

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directrix y^2+6y-2x+13=0

directrix

y^{2} + 6 y - 2 x + 13 = 0

x = \frac{3}{2}

Solution steps

Rewrite

y^{2} + 6 y - 2 x + 13 = 0

in the standard form

4 \cdot \frac{1}{2} (x - 2) = (y - (- 3))^{2}

(h, k) = (2, - 3), p = \frac{1}{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, - 3)

x-coordinate

x = 2 - p

x = 2 - \frac{1}{2}

Refine

x = \frac{3}{2}

\frac{x ^{2}}{49} + \frac{y ^{2}}{16} = 1

f (x) = x^{2} + 2 x - 8

\frac{x ^{2}}{36} - \frac{y ^{2}}{9} = 1

y = x^{2}

f (x) = x^{2} - 4 x - 12