What is the directrix y=(6x-1)(3x-2) ?

The directrix y=(6x-1)(3x-2) is y=-41/36

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directrix y=(6x-1)(3x-2)

directrix

y = (6 x - 1) (3 x - 2)

y = - \frac{41}{36}

Solution steps

Rewrite

y = (6 x - 1) (3 x - 2)

in the standard form

4 \cdot \frac{1}{72} (y - (- \frac{9}{8})) = (x - \frac{5}{12})^{2}

(h, k) = (\frac{5}{12}, - \frac{9}{8}), p = \frac{1}{72}

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{5}{12}, - \frac{9}{8})

y-coordinate

y = - \frac{9}{8} - p

y = - \frac{9}{8} - \frac{1}{72}

Refine

y = - \frac{41}{36}

y = \frac{x ^{2}}{32}

3 y^{2} - 4 x - 6 y + 23 = 0

x^{2} + 4 x - 5

x = \frac{- 1}{4} (y + 2)^{2}

x^{2} - x - 56