What is the directrix y^2-5x+12y=-16 ?

The directrix y^2-5x+12y=-16 is x=-21/4

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directrix y^2-5x+12y=-16

directrix

y^{2} - 5 x + 12 y = - 16

x = - \frac{21}{4}

Solution steps

Rewrite

y^{2} - 5 x + 12 y = - 16

in the standard form

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

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

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, - 6)

x-coordinate

x = - 4 - p

x = - 4 - \frac{5}{4}

Refine

x = - \frac{21}{4}

3 y^{2} = 10 x

4 x^{2} - 5 x + 6

3 x^{2} + x - 5

(y - 0)^{2} = - 4 \cdot 0.01 (x - 0)

3 x^{2} - 10 x + 3