What is the directrix y^2-6y-4x+5=0 ?

The directrix y^2-6y-4x+5=0 is x=-2

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directrix y^2-6y-4x+5=0

directrix

y^{2} - 6 y - 4 x + 5 = 0

x = - 2

Solution steps

Rewrite

y^{2} - 6 y - 4 x + 5 = 0

in the standard form

4 \cdot 1 \cdot (x - (- 1)) = (y - 3)^{2}

(h, k) = (- 1, 3), p = 1

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

(- 1, 3)

x-coordinate

x = - 1 - p

x = - 1 - 1

Refine

x = - 2

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

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

- \frac{1}{4} x^{2} + 8 x - 4

y^{2} = 10 x

x^{2} + 1