What is the directrix-1/3 (x-3)=(y+5)^2 ?

The directrix-1/3 (x-3)=(y+5)^2 is x= 37/12

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directrix-1/3 (x-3)=(y+5)^2

directrix

- \frac{1}{3} (x - 3) = (y + 5)^{2}

x = \frac{37}{12}

Solution steps

Rewrite

- \frac{1}{3} (x - 3) = (y + 5)^{2}

in the standard form:

4 (- \frac{1}{12}) (x - 3) = (y - (- 5))^{2}

(h, k) = (3, - 5), p = - \frac{1}{12}

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

(3, - 5)

x-coordinate

x = 3 - p

x = 3 - (- \frac{1}{12})

Refine

x = \frac{37}{12}

+ 2.5 t^{2} + 6 t

y = x^{2} + 6 x + 8

- 5 t^{2} + 20 t

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

y^{2} - 2 y - 12 x + 25 = 0

What is the directrix-1/3 (x-3)=(y+5)^2 ?
The directrix-1/3 (x-3)=(y+5)^2 is x= 37/12