What is the foci x^2-20y-2x-39=0 ?

The foci x^2-20y-2x-39=0 is (1,3)

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foci x^2-20y-2x-39=0

foci

x^{2} - 20 y - 2 x - 39 = 0

(1, 3)

Solution steps

Rewrite

x^{2} - 20 y - 2 x - 39 = 0

in the standard form

4 \cdot 5 (y - (- 2)) = (x - 1)^{2}

(h, k) = (1, - 2), p = 5

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

p

from the center

(1, - 2)

along the y-axis

(1, - 2 + p)

= (1, - 2 + 5)

Refine

(1, 3)

y^{2} + x + y = 0

y = (x + 1) (x + 2)

3 x^{2} - 16 x + 5

y^{2} - 12 y + 6 x + 36 = 0

x^{2} - 6 x - 20 y - 11 = 0