What is the directrix 4x^2+48y+12x=159 ?

The directrix 4x^2+48y+12x=159 is y= 13/2

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directrix 4x^2+48y+12x=159

directrix

4 x^{2} + 48 y + 12 x = 159

y = \frac{13}{2}

Solution steps

Rewrite

4 x^{2} + 48 y + 12 x = 159

in the standard form

4 (- 3) (y - \frac{7}{2}) = (x - (- \frac{3}{2}))^{2}

(h, k) = (- \frac{3}{2}, \frac{7}{2}), p = - 3

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

(- \frac{3}{2}, \frac{7}{2})

y-coordinate

y = \frac{7}{2} - p

y = \frac{7}{2} - (- 3)

Refine

y = \frac{13}{2}

(x - 3)^{2} = - 8 (y + 2)

4 x^{2} - 2 x

y = - x^{2} + 18 x - 79

y = (x - 2)^{2} - 7

y > x^{2} - 3

What is the directrix 4x^2+48y+12x=159 ?
The directrix 4x^2+48y+12x=159 is y= 13/2