What is the directrix 2(x^2+6x)+5y+8=0 ?

The directrix 2(x^2+6x)+5y+8=0 is y= 21/8

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directrix 2(x^2+6x)+5y+8=0

directrix

2 (x^{2} + 6 x) + 5 y + 8 = 0

y = \frac{21}{8}

Solution steps

Rewrite

2 (x^{2} + 6 x) + 5 y + 8 = 0

in the standard form

4 (- \frac{5}{8}) (y - 2) = (x - (- 3))^{2}

(h, k) = (- 3, 2), p = - \frac{5}{8}

Parabola is symmetric around the y-axis and so the directrix is a line parallel to the x-axis, a distance

- p

from the center

(- 3, 2)

y-coordinate

y = 2 - p

y = 2 - (- \frac{5}{8})

Refine

y = \frac{21}{8}

10 x^{2}

- 4 x^{2} - 2 x + 1

(x + 5)^{2} = 12 (y - 2)

y^{2} + 4 x - 80 y + 20 = 0

- x^{2} - 4 x + 1

What is the directrix 2(x^2+6x)+5y+8=0 ?
The directrix 2(x^2+6x)+5y+8=0 is y= 21/8