What is the directrix y^2+2y+1=-2x+4 ?

The directrix y^2+2y+1=-2x+4 is x= 5/2

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directrix y^2+2y+1=-2x+4

directrix

y^{2} + 2 y + 1 = - 2 x + 4

x = \frac{5}{2}

Solution steps

Rewrite

y^{2} + 2 y + 1 = - 2 x + 4

in the standard form

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

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

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

(2, - 1)

x-coordinate

x = 2 - p

x = 2 - (- \frac{1}{2})

Refine

x = \frac{5}{2}

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

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

2 x^{2} - 19 x + 9

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

x^{2} + 4