What is the directrix y^2+2x+6y+17=0 ?

The directrix y^2+2x+6y+17=0 is x=-7/2

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directrix y^2+2x+6y+17=0

directrix

y^{2} + 2 x + 6 y + 17 = 0

x = - \frac{7}{2}

Solution steps

Rewrite

y^{2} + 2 x + 6 y + 17 = 0

in the standard form

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

(h, k) = (- 4, - 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

(- 4, - 3)

x-coordinate

x = - 4 - p

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

Refine

x = - \frac{7}{2}

(x - 7)^{2}

- 3 x^{2} + 75

y = \frac{95 x ^{2} - 10 x + 26}{10}

y = 64 x^{2}

x^{2} + 2 x - 1 - (2 x^{2} - 3 x + 6)