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

The directrix x^2-6x+5y=34 is y= 197/20

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

directrix

y = \frac{197}{20}

Solution steps

Rewrite

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

in the standard form

4 (- \frac{5}{4}) (y - \frac{43}{5}) = (x - 3)^{2}

(h, k) = (3, \frac{43}{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, \frac{43}{5})

y-coordinate

y = \frac{43}{5} - p

y = \frac{43}{5} - (- \frac{5}{4})

Refine

y = \frac{197}{20}