What is the foci x^2-6x-20y-11=0 ?

The foci x^2-6x-20y-11=0 is (3,4)

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foci x^2-6x-20y-11=0

foci

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

(3, 4)

Solution steps

Rewrite

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

in the standard form

4 \cdot 5 (y - (- 1)) = (x - 3)^{2}

(h, k) = (3, - 1), p = 5

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

p

from the center

(3, - 1)

along the y-axis

(3, - 1 + p)

= (3, - 1 + 5)

Refine

(3, 4)

y = 3 x^{2} - 36 x + 81

(y - 6)^{2}

y = (x - 2)^{2} - 4

y^{2} = - 6 (x - 3)

y = x^{2} + 7 x - 1