What is the directrix 4x^2-20x-24y+97=0 ?

The directrix 4x^2-20x-24y+97=0 is y= 3/2

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directrix 4x^2-20x-24y+97=0

directrix

4 x^{2} - 20 x - 24 y + 97 = 0

y = \frac{3}{2}

Solution steps

Rewrite

4 x^{2} - 20 x - 24 y + 97 = 0

in the standard form

4 \cdot \frac{3}{2} (y - 3) = (x - \frac{5}{2})^{2}

(h, k) = (\frac{5}{2}, 3), p = \frac{3}{2}

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)

y-coordinate

y = 3 - p

y = 3 - \frac{3}{2}

Refine

y = \frac{3}{2}

\frac{6 x}{7} \frac{4 x}{3}

x^{2} - x - 6

y = (x + 4)^{2}

y = x^{2} + 2 x - 1 - (2 x^{2} - 3 x + 6)

y = 2250 (0.015 - 0.001 x)^{2} + 6000 x

What is the directrix 4x^2-20x-24y+97=0 ?
The directrix 4x^2-20x-24y+97=0 is y= 3/2