What is the foci 9x^2-18x+25y^2-250y+409=0 ?

The foci 9x^2-18x+25y^2-250y+409=0 is (5,5),(-3,5)

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foci 9x^2-18x+25y^2-250y+409=0

foci

9 x^{2} - 18 x + 25 y^{2} - 250 y + 409 = 0

(5, 5), (- 3, 5)

Solution steps

(h + c, k), (h - c, k)

Calculate ellipse properties

9 x^{2} - 18 x + 25 y^{2} - 250 y + 409 = 0 :

Ellipse with center

(h, k) = (1, 5), a = 5, b = 3

(1 + c, 5), (1 - c, 5)

Compute

c :

c = 5^{2} - 3^{2} : 4

(1 + 4, 5), (1 - 4, 5)

Refine

(5, 5), (- 3, 5)

25 x^{2} + 9 y^{2} + 50 x - 108 y + 124 = 0

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

\frac{x ^{2}}{3} + \frac{y ^{2}}{5} = 1

16 x^{2} + 25 y^{2} - 64 x + 150 y - 111 = 0

9 x^{2} + 49 y^{2} = 441

What is the foci 9x^2-18x+25y^2-250y+409=0 ?
The foci 9x^2-18x+25y^2-250y+409=0 is (5,5),(-3,5)