What is the directrix x^2-8x+63/4 ?

The directrix x^2-8x+63/4 is y=-1/2

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directrix x^2-8x+63/4

directrix

x^{2} - 8 x + \frac{63}{4}

y = - \frac{1}{2}

Solution steps

Rewrite

y = x^{2} - 8 x + \frac{63}{4}

in the standard form

4 \cdot \frac{1}{4} (y - (- \frac{1}{4})) = (x - 4)^{2}

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

(4, - \frac{1}{4})

y-coordinate

y = - \frac{1}{4} - p

y = - \frac{1}{4} - \frac{1}{4}

Refine

y = - \frac{1}{2}

x^{2} = - 2 y

\frac{1}{4} x^{2}

3 y^{2} - 30 y + 77

(x - 3)^{2} + 1

x^{2} = - 6 y