What is the directrix x=y^2-y-42 ?

The directrix x=y^2-y-42 is x=-85/2

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directrix x=y^2-y-42

directrix

x = y^{2} - y - 42

x = - \frac{85}{2}

Solution steps

Rewrite

x = y^{2} - y - 42

in the standard form

4 \cdot \frac{1}{4} (x - (- \frac{169}{4})) = (y - \frac{1}{2})^{2}

(h, k) = (- \frac{169}{4}, \frac{1}{2}), p = \frac{1}{4}

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{169}{4}, \frac{1}{2})

x-coordinate

x = - \frac{169}{4} - p

x = - \frac{169}{4} - \frac{1}{4}

Refine

x = - \frac{85}{2}

x^{2} - 4 x - 8 y + 2 = 0

(3 x - 4) (4 x - 3) - 2 x

(x - 3)^{2} = - 12 y

x^{2} = 10 y

y = 6 x^{2} - 3 x 5