What is the directrix y^2=5y+7x+3 ?

The directrix y^2=5y+7x+3 is x=-43/14

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directrix y^2=5y+7x+3

directrix

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

x = - \frac{43}{14}

Solution steps

Rewrite

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

in the standard form

4 \cdot \frac{7}{4} (x - (- \frac{37}{28})) = (y - \frac{5}{2})^{2}

(h, k) = (- \frac{37}{28}, \frac{5}{2}), p = \frac{7}{4}

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

(- \frac{37}{28}, \frac{5}{2})

x-coordinate

x = - \frac{37}{28} - p

x = - \frac{37}{28} - \frac{7}{4}

Refine

x = - \frac{43}{14}

2 y^{2} - 12 y - x + 5 = 0

- 0.03 x^{2} + 45 x + 124.5

- x^{2} - 4 x

4 y^{2} - 12 y + 56 x + 177 = 0

3 x^{2} + 19 x - 40