What is the foci 3x^2+2y=26 ?

The foci 3x^2+2y=26 is (0, 77/6)

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foci 3x^2+2y=26

foci

3 x^{2} + 2 y = 26

(0, \frac{77}{6})

Solution steps

Rewrite

3 x^{2} + 2 y = 26

in the standard form:

4 (- \frac{1}{6}) (y - 13) = (x - 0)^{2}

(h, k) = (0, 13), p = - \frac{1}{6}

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

p

from the center

(0, 13)

along the y-axis

(0, 13 + p)

= (0, 13 + (- \frac{1}{6}))

Refine

(0, \frac{77}{6})

y^{2} = - 2 x

x^{2} + y^{2} - 4 x + 10 y + 13 = 0

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

\frac{y ^{2}}{9} - \frac{x ^{2}}{16} = 1

x = 3 y^{2}