What is the foci x^2-10x-24y=-25-24 ?

The foci x^2-10x-24y=-25-24 is (5,7)

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foci x^2-10x-24y=-25-24

foci

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

(5, 7)

Solution steps

Rewrite

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

in the standard form

4 \cdot 6 (y - 1) = (x - 5)^{2}

(h, k) = (5, 1), p = 6

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

p

from the center

(5, 1)

along the y-axis

(5, 1 + p)

= (5, 1 + 6)

Refine

(5, 7)

x^{2} = 8 (y - 2)

x^{2} - 2 x + 5

(y - 2)^{2} = 8 (x - 5)

(x + 1)^{2} = (y + 4)

y = - x^{2} + 4 x + 3