What is the foci x=3(y-2)^2-7 ?

The foci x=3(y-2)^2-7 is (-83/12 ,2)

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foci x=3(y-2)^2-7

foci

x = 3 (y - 2)^{2} - 7

(- \frac{83}{12}, 2)

Solution steps

Rewrite

x = 3 (y - 2)^{2} - 7

in the standard form:

4 \cdot \frac{1}{12} (x - (- 7)) = (y - 2)^{2}

(h, k) = (- 7, 2), p = \frac{1}{12}

Parabola is symmetric around the x-axis and so the focus lies a distance

p

from the center

(- 7, 2)

along the x-axis

(- 7 + p, 2)

= (- 7 + \frac{1}{12}, 2)

Refine

(- \frac{83}{12}, 2)

3 x^{2} + 2 x + 6

\frac{1}{8} x^{2} - y = 0

- x^{2} + 4 y - 44 = - 8 x

- x^{2} - 2 x + 3

x - 2 = 3 (y - 5)^{2}