What is the directrix x=(2y-1)(5y-6) ?

The directrix x=(2y-1)(5y-6) is x=-5/4

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directrix x=(2y-1)(5y-6)

directrix

x = (2 y - 1) (5 y - 6)

x = - \frac{5}{4}

Solution steps

Rewrite

x = (2 y - 1) (5 y - 6)

in the standard form

4 \cdot \frac{1}{40} (x - (- \frac{49}{40})) = (y - \frac{17}{20})^{2}

(h, k) = (- \frac{49}{40}, \frac{17}{20}), p = \frac{1}{40}

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

(- \frac{49}{40}, \frac{17}{20})

x-coordinate

x = - \frac{49}{40} - p

x = - \frac{49}{40} - \frac{1}{40}

Refine

x = - \frac{5}{4}

+ 2 (x + 1)^{2} - 3

x^{2} - 6 y = 0

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

y = x^{2} - 10 x + 25

y = x^{2} + 10 x - 96