What is the directrix y=(x-(24)/(x+2))(x-(12)/(x-4)) ?

The directrix y=(x-(24)/(x+2))(x-(12)/(x-4)) is y=-145/4

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directrix y=(x-(24)/(x+2))(x-(12)/(x-4))

directrix

y = (x - \frac{24}{x + 2}) (x - \frac{12}{x - 4})

y = - \frac{145}{4}

Solution steps

Rewrite

y = (x - \frac{24}{x + 2}) (x - \frac{12}{x - 4})

in the standard form

4 \cdot \frac{1}{4} (y - (- 36)) = (x - 0)^{2}

(h, k) = (0, - 36), p = \frac{1}{4}

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

(0, - 36)

y-coordinate

y = - 36 - p

y = - 36 - \frac{1}{4}

Refine

y = - \frac{145}{4}

x = (y + 1) y

(x - 9)^{2} - 6

x^{2} - 16 y = 0

0.8 x^{2} + 500 x - 25000

9 x^{2}

What is the directrix y=(x-(24)/(x+2))(x-(12)/(x-4)) ?
The directrix y=(x-(24)/(x+2))(x-(12)/(x-4)) is y=-145/4