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}

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

x^{2} - 3 x - 4

(x - 4)^{2} = 8 (y + 2)

- \frac{1}{8} (y - 8)^{2} + 2

2 x^{2} - 10

What is the directrix x^{(2)}-6x+5y=-34 ?
The directrix x^{(2)}-6x+5y=-34 is y=-15/4