What is the directrix x^2-6x+5y=-34 ?

The directrix x^2-6x+5y=-34 is y=-15/4

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directrix x^2-6x+5y=-34

directrix

x^{2} - 6 x + 5 y = - 34

y = - \frac{15}{4}

Solution steps

Rewrite

x^{2} - 6 x + 5 y = - 34

in the standard form

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

(h, k) = (3, - 5), p = - \frac{5}{4}

Parabola is symmetric around the y-axis and so the directrix is a line parallel to the x-axis, a distance

- p

from the center

(3, - 5)

y-coordinate

y = - 5 - p

y = - 5 - (- \frac{5}{4})

Refine

y = - \frac{15}{4}

y^{2} - 8 x = 0

x^{2} + 8 x + 18

(y - 2)^{2} = 12 (x + 1)

y = x^{2} - 5 x - 24

y = - 4 (x + 10)^{2} + 6