What is the directrix y^2-10y-12x+37=0 ?

The directrix y^2-10y-12x+37=0 is x=-2

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directrix y^2-10y-12x+37=0

directrix

y^{2} - 10 y - 12 x + 37 = 0

x = - 2

Solution steps

Rewrite

y^{2} - 10 y - 12 x + 37 = 0

in the standard form

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

(h, k) = (1, 5), p = 3

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, 5)

x-coordinate

x = 1 - p

x = 1 - 3

Refine

x = - 2

\frac{x}{25} - y^{2} = 1

y = x^{2} - 10 x - 31

3 x^{2} - 24 x - 15

(x + 4)^{2} = 12 y - 24

x^{2} - 2 x - 9