What is the foci 9x^2+49y^2-144x+490y+1360=0 ?

The foci 9x^2+49y^2-144x+490y+1360=0 is (8+2sqrt(10),-5),(8-2sqrt(10),-5)

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foci 9x^2+49y^2-144x+490y+1360=0

foci

9 x^{2} + 49 y^{2} - 144 x + 490 y + 1360 = 0

(8 + 210, - 5), (8 - 210, - 5)

Solution steps

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

Calculate ellipse properties

9 x^{2} + 49 y^{2} - 144 x + 490 y + 1360 = 0 :

Ellipse with center

(h, k) = (8, - 5), a = 7, b = 3

(8 + c, - 5), (8 - c, - 5)

Compute

c :

c = 7^{2} - 3^{2} : 210

(8 + 210, - 5), (8 - 210, - 5)

9 x^{2} + 18 x + 4 y^{2} - 24 y + 9 = 0

x^{2} + 4 y^{2} - 6 x + 20 y - 2 = 0

\frac{( x + 2 ) ^{2}}{9} + \frac{( y - 1 ) ^{2}}{16} = 1

4 x^{2} + y^{2} - 8 x + 4 y - 8 = 0

25 x^{2} + 144 y^{2} = 900

What is the foci 9x^2+49y^2-144x+490y+1360=0 ?
The foci 9x^2+49y^2-144x+490y+1360=0 is (8+2sqrt(10),-5),(8-2sqrt(10),-5)