What is the directrix (y-7)^2=-12(x+1) ?

The directrix (y-7)^2=-12(x+1) is x=2

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directrix (y-7)^2=-12(x+1)

directrix

(y - 7)^{2} = - 12 (x + 1)

x = 2

Solution steps

Rewrite

(y - 7)^{2} = - 12 (x + 1)

in the standard form:

4 (- 3) (x - (- 1)) = (y - 7)^{2}

(h, k) = (- 1, 7), 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

(- 1, 7)

x-coordinate

x = - 1 - p

x = - 1 - (- 3)

Refine

x = 2

x^{2} = - 16 y

x^{2}

\frac{( x - 3 ) ^{2}}{5} + \frac{( y - 1 ) ^{2}}{15} = 1

\frac{x ^{2}}{100} + \frac{y ^{2}}{64} = 1

\frac{x ^{2}}{4} + \frac{y ^{2}}{16} = 1