What is the directrix 5x^2+30x+24y=51 ?

The directrix 5x^2+30x+24y=51 is y= 26/5

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directrix 5x^2+30x+24y=51

directrix

5 x^{2} + 30 x + 24 y = 51

y = \frac{26}{5}

Solution steps

Rewrite

5 x^{2} + 30 x + 24 y = 51

in the standard form

4 (- \frac{6}{5}) (y - 4) = (x - (- 3))^{2}

(h, k) = (- 3, 4), p = - \frac{6}{5}

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, 4)

y-coordinate

y = 4 - p

y = 4 - (- \frac{6}{5})

Refine

y = \frac{26}{5}

x^{2} - 2 x - 4 y + 9 = 0

\frac{- 3 x ^{2} - 2 x + 6}{5}

3 x^{2} - x - 2

y = - 3 x^{2} - 12 x - 9

y = \frac{1}{8} x^{2}

What is the directrix 5x^2+30x+24y=51 ?
The directrix 5x^2+30x+24y=51 is y= 26/5