What is the directrix x^2-4x-5y+7=0 ?

The directrix x^2-4x-5y+7=0 is y=-13/20

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directrix x^2-4x-5y+7=0

directrix

x^{2} - 4 x - 5 y + 7 = 0

y = - \frac{13}{20}

Solution steps

Rewrite

x^{2} - 4 x - 5 y + 7 = 0

in the standard form

4 \cdot \frac{5}{4} (y - \frac{3}{5}) = (x - 2)^{2}

(h, k) = (2, \frac{3}{5}), p = \frac{5}{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

(2, \frac{3}{5})

y-coordinate

y = \frac{3}{5} - p

y = \frac{3}{5} - \frac{5}{4}

Refine

y = - \frac{13}{20}

+ x^{2} + 4 x + 6

\frac{( x - 3 ) ^{2}}{8} + 5

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

(y + 1)^{2} = 12 x

(y - 2)^{2} = 40 (x - 2)