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

The directrix x=2y^2-1-(5y-6) is x= 7/4

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

directrix

x = \frac{7}{4}

Solution steps

Rewrite

x = 2 y^{2} - 1 - (5 y - 6)

in the standard form

4 \cdot \frac{1}{8} (x - \frac{15}{8}) = (y - \frac{5}{4})^{2}

(h, k) = (\frac{15}{8}, \frac{5}{4}), p = \frac{1}{8}

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{15}{8}, \frac{5}{4})

x-coordinate

x = \frac{15}{8} - p

x = \frac{15}{8} - \frac{1}{8}

Refine

x = \frac{7}{4}