What is the foci y=6x^2+26x+8 ?

The foci y=6x^2+26x+8 is (-13/6 ,-161/8)

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foci y=6x^2+26x+8

foci

y = 6 x^{2} + 26 x + 8

(- \frac{13}{6}, - \frac{161}{8})

Solution steps

Rewrite

y = 6 x^{2} + 26 x + 8

in the standard form

4 \cdot \frac{1}{24} (y - (- \frac{121}{6})) = (x - (- \frac{13}{6}))^{2}

(h, k) = (- \frac{13}{6}, - \frac{121}{6}), p = \frac{1}{24}

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

p

from the center

(- \frac{13}{6}, - \frac{121}{6})

along the y-axis

(- \frac{13}{6}, - \frac{121}{6} + p)

= (- \frac{13}{6}, - \frac{121}{6} + \frac{1}{24})

Refine

(- \frac{13}{6}, - \frac{161}{8})

y = x^{2} + 7 x + 10

y = (2 x - 1) (4 x - 1)

(y + 6)^{2} = 12 (x + 1)

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

x^{2} - 8 y = 0