What is the directrix y^2-10y+4x+25=0 ?

The directrix y^2-10y+4x+25=0 is x=1

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directrix y^2-10y+4x+25=0

directrix

y^{2} - 10 y + 4 x + 25 = 0

x = 1

Solution steps

Rewrite

y^{2} - 10 y + 4 x + 25 = 0

in the standard form

4 (- 1) (x - 0) = (y - 5)^{2}

(h, k) = (0, 5), 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

(0, 5)

x-coordinate

x = 0 - p

x = 0 - (- 1)

Refine

x = 1

(x + 4)^{2} = - 6 (y - 3)

(x - 3)^{2} = \frac{1}{2} (y + 1)

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

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

- x^{2} + 2 x - 3