What is the directrix 4t-9t^2 ?

The directrix 4t-9t^2 is y= 17/36

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directrix 4t-9t^2

directrix

4 t - 9 t^{2}

y = \frac{17}{36}

Solution steps

Rewrite

y = 4 t - 9 t^{2}

in the standard form

4 (- \frac{1}{36}) (y - \frac{4}{9}) = (t - \frac{2}{9})^{2}

(h, k) = (\frac{2}{9}, \frac{4}{9}), p = - \frac{1}{36}

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

(\frac{2}{9}, \frac{4}{9})

y-coordinate

y = \frac{4}{9} - p

y = \frac{4}{9} - (- \frac{1}{36})

Refine

y = \frac{17}{36}

y = (x + 2)^{2} - 3

- 2 x^{2} + 12 x - 2

4 x^{2} - 8 x - 3

y = - 9 x^{2}

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