What is the foci x^2-2x-8y-31=0 ?

The foci x^2-2x-8y-31=0 is (1,-2)

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foci x^2-2x-8y-31=0

foci

x^{2} - 2 x - 8 y - 31 = 0

(1, - 2)

Solution steps

Rewrite

x^{2} - 2 x - 8 y - 31 = 0

in the standard form

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

(h, k) = (1, - 4), p = 2

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

p

from the center

(1, - 4)

along the y-axis

(1, - 4 + p)

= (1, - 4 + 2)

Refine

(1, - 2)

5 x^{2}

y = x^{2} - x + 1

(x + \frac{3}{5}) (x - \frac{2}{5})

+ \frac{y ^{3} - 100 y}{y + 10}

x^{2} - 10 x - 24 y = - 25 - 24