What is the directrix 3x^2+2 ?

The directrix 3x^2+2 is y= 23/12

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directrix 3x^2+2

directrix

3 x^{2} + 2

y = \frac{23}{12}

Solution steps

Rewrite

y = 3 x^{2} + 2

in the standard form:

4 \cdot \frac{1}{12} (y - 2) = (x - 0)^{2}

(h, k) = (0, 2), p = \frac{1}{12}

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

(0, 2)

y-coordinate

y = 2 - p

y = 2 - \frac{1}{12}

Refine

y = \frac{23}{12}

5 x^{2} + 7 y = 3

x = 4 y^{2} + 12 y + 9

7 x^{2} - 5 x + 9

- 8 x^{2} + 4 x

3 y + 4 x = - 2 x^{2} - 14