What is the foci-25x^2+4y^2+150x+24y-289=0 ?

The foci-25x^2+4y^2+150x+24y-289=0 is (3,-3+sqrt(29)),(3,-3-sqrt(29))

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foci-25x^2+4y^2+150x+24y-289=0

foci

- 25 x^{2} + 4 y^{2} + 150 x + 24 y - 289 = 0

(3, - 3 + 29), (3, - 3 - 29)

Solution steps

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

Calculate Hyperbola properties

- 25 x^{2} + 4 y^{2} + 150 x + 24 y - 289 = 0 :

Up-down Hyperbola with

(h, k) = (3, - 3), a = 5, b = 2

(3, - 3 + c), (3, - 3 - c)

Compute

c :

c = 5^{2} + 2^{2} : 29

(3, - 3 + 29), (3, - 3 - 29)

9 x^{2} - 16 y^{2} + 36 x + 32 y - 124 = 0

- \frac{x ^{2}}{a ^{2}} + \frac{y ^{2}}{b ^{2}} = 1

100 x^{2} + 112952 x - 100 y^{2} - 106 y = 48838

4 x^{2} - 25 y^{2} + 16 x + 50 y - 109 = 0

9 x^{2} - 18 x - 24 y - 63 = 4 y^{2}

What is the foci-25x^2+4y^2+150x+24y-289=0 ?
The foci-25x^2+4y^2+150x+24y-289=0 is (3,-3+sqrt(29)),(3,-3-sqrt(29))