What is the directrix y^2-10x+4y-16=0 ?

The directrix y^2-10x+4y-16=0 is x=-9/2

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directrix y^2-10x+4y-16=0

directrix

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

x = - \frac{9}{2}

Solution steps

Rewrite

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

in the standard form

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

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

Parabola is symmetric around the x-axis and so the directrix is a line parallel to the y-axis, a distance

- p

from the center

(- 2, - 2)

x-coordinate

x = - 2 - p

x = - 2 - \frac{5}{2}

Refine

x = - \frac{9}{2}

- 4 x^{2} + 6 x - 1

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

y = - 4 x^{2} - 4

(x - 4)^{2} = - 8 (y + 3)

y^{2} + 33 = - 8 x - 23