What is the directrix y^2+12x+4y-32=0 ?

The directrix y^2+12x+4y-32=0 is x=6

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directrix y^2+12x+4y-32=0

directrix

y^{2} + 12 x + 4 y - 32 = 0

x = 6

Solution steps

Rewrite

y^{2} + 12 x + 4 y - 32 = 0

in the standard form

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

(h, k) = (3, - 2), p = - 3

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

(3, - 2)

x-coordinate

x = 3 - p

x = 3 - (- 3)

Refine

x = 6

x^{2} + y^{2} - 18 x - 14 y + 124 = 0

\frac{x ^{2}}{9} + \frac{y ^{2}}{25} = 1

9 (x - 1)^{2} - 16 (y + 2)^{2} = 144

9 x^{2} + 4 y^{2} + 36 x - 24 y + 36 = 0

f (x) = 3 x^{2} - 18 x + 23