What is the directrix-5t^2+20t ?

The directrix-5t^2+20t is y= 401/20

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directrix-5t^2+20t

directrix

- 5 t^{2} + 20 t

y = \frac{401}{20}

Solution steps

Rewrite

y = - 5 t^{2} + 20 t

in the standard form

4 (- \frac{1}{20}) (y - 20) = (t - 2)^{2}

(h, k) = (2, 20), 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

(2, 20)

y-coordinate

y = 20 - p

y = 20 - (- \frac{1}{20})

Refine

y = \frac{401}{20}

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

y^{2} - 2 y - 12 x + 25 = 0

y^{2} - 6 x - y + 11 = 0

4 (x + 1)^{2}

x^{2} + 5 x - 24