What is the directrix y=5x^2+210x-34775 ?

The directrix y=5x^2+210x-34775 is y=-739601/20

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directrix y=5x^2+210x-34775

directrix

y = 5 x^{2} + 210 x - 34775

y = - \frac{739601}{20}

Solution steps

Rewrite

y = 5 x^{2} + 210 x - 34775

in the standard form

4 \cdot \frac{1}{20} (y - (- 36980)) = (x - (- 21))^{2}

(h, k) = (- 21, - 36980), p = \frac{1}{20}

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

(- 21, - 36980)

y-coordinate

y = - 36980 - p

y = - 36980 - \frac{1}{20}

Refine

y = - \frac{739601}{20}

y^{2} - 6 y - 4 x + 5 = 0

(x + 2)^{2} = - 6 (y - 1)

y = - x^{2} + 5 x - 7

- \frac{1}{4} x^{2} + 8 x - 4

y^{2} = 10 x

What is the directrix y=5x^2+210x-34775 ?
The directrix y=5x^2+210x-34775 is y=-739601/20