What is the foci y^2-12x-2y-25=0 ?

The foci y^2-12x-2y-25=0 is (5/6 ,1)

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foci y^2-12x-2y-25=0

foci

y^{2} - 12 x - 2 y - 25 = 0

(\frac{5}{6}, 1)

Solution steps

Rewrite

y^{2} - 12 x - 2 y - 25 = 0

in the standard form

4 \cdot 3 (x - (- \frac{13}{6})) = (y - 1)^{2}

(h, k) = (- \frac{13}{6}, 1), p = 3

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

p

from the center

(- \frac{13}{6}, 1)

along the x-axis

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

= (- \frac{13}{6} + 3, 1)

Refine

(\frac{5}{6}, 1)

y = 4 x^{2} + 8 x - 20

x = - \frac{1}{52} (y^{2} + 18 y - 647)

4 x^{2} + 8 x

x^{2} - 13 x + 40

- 2 x^{2} - 8 x - 12