What is the directrix (x-5/2)^2=7(y+3.75) ?

The directrix (x-5/2)^2=7(y+3.75) is y=-5.5

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directrix (x-5/2)^2=7(y+3.75)

directrix

(x - \frac{5}{2})^{2} = 7 (y + 3.75)

y = - 5.5

Solution steps

Rewrite

(x - \frac{5}{2})^{2} = 7 (y + 3.75)

in the standard form:

4 \cdot \frac{7}{4} (y - (- 3.75)) = (x - \frac{5}{2})^{2}

(h, k) = (\frac{5}{2}, - 3.75), p = \frac{7}{4}

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{5}{2}, - 3.75)

y-coordinate

y = - 3.75 - p

y = - 3.75 - \frac{7}{4}

Refine

y = - 5.5

y = - x^{2} + 8 x - 18

11 x^{2} - 8

y = 7 x^{2} + 5

x^{2} + 3 x + 4

y^{2} = - x

What is the directrix (x-5/2)^2=7(y+3.75) ?
The directrix (x-5/2)^2=7(y+3.75) is y=-5.5