What is the directrix 0.3+5.5t-4.9t^2 ?

The directrix 0.3+5.5t-4.9t^2 is y=1.89438…

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directrix 0.3+5.5t-4.9t^2

directrix

0.3 + 5.5 t - 4.9 t^{2}

y = 1.89438 \dots

Solution steps

Rewrite

y = 0.3 + 5.5 t - 4.9 t^{2}

in the standard form

4 (- 0.05102 \dots) (y - 1.84336 \dots) = (t - 0.56122 \dots)^{2}

(h, k) = (0.56122 \dots, 1.84336 \dots), p = - 0.05102 \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

(0.56122 \dots, 1.84336 \dots)

y-coordinate

y = 1.84336 \dots - p

y = 1.84336 \dots - (- 0.05102 \dots)

Refine

y = 1.89438 \dots

y + 8 x^{2} = 0

- 3 (x - 7)^{2}

(x + 7)^{2} = 5 (y + 3)

y^{2} - 6 y = - 4 x + 3

+ x^{2} - 14

What is the directrix 0.3+5.5t-4.9t^2 ?
The directrix 0.3+5.5t-4.9t^2 is y=1.89438…