What is the directrix y=(2X+5)(3X-7) ?

The directrix y=(2X+5)(3X-7) is y=-421/12

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directrix y=(2X+5)(3X-7)

directrix

y = (2 X + 5) (3 X - 7)

y = - \frac{421}{12}

Solution steps

Rewrite

y = (2 X + 5) (3 X - 7)

in the standard form

4 \cdot \frac{1}{24} (y - (- \frac{841}{24})) = (X - (- \frac{1}{12}))^{2}

(h, k) = (- \frac{841}{24}, - \frac{1}{12}), p = \frac{1}{24}

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{841}{24}, - \frac{1}{12})

x-coordinate

y = - \frac{841}{24} - p

y = - \frac{841}{24} - \frac{1}{24}

Refine

y = - \frac{421}{12}

(y + 2)^{2} = - 16 (x + 9)

x^{2} + 5 x - 84

2 x^{2} - 32 x - y + 127 = 0

y^{2} + 2 x + 6 y + 17 = 0

(x - 7)^{2}

What is the directrix y=(2X+5)(3X-7) ?
The directrix y=(2X+5)(3X-7) is y=-421/12