What is the directrix 1.5+17.67t-4.905t^2 ?

The directrix 1.5+17.67t-4.905t^2 is y=17.46477…

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directrix 1.5+17.67t-4.905t^2

directrix

1.5 + 17.67 t - 4.905 t^{2}

y = 17.46477 \dots

Solution steps

Rewrite

y = 1.5 + 17.67 t - 4.905 t^{2}

in the standard form

4 (- 0.05096 \dots) (y - 17.41380 \dots) = (t - 1.80122 \dots)^{2}

(h, k) = (1.80122 \dots, 17.41380 \dots), p = - 0.05096 \dots

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

(1.80122 \dots, 17.41380 \dots)

y-coordinate

y = 17.41380 \dots - p

y = 17.41380 \dots - (- 0.05096 \dots)

Refine

y = 17.46477 \dots

x^{2} = 32 y

y = (x + 6) (x - 2)

6 x^{2} + 7 x - 3

x = - 4 y^{2}

y^{2} - 10 x + 4 y - 16 = 0

What is the directrix 1.5+17.67t-4.905t^2 ?
The directrix 1.5+17.67t-4.905t^2 is y=17.46477…