What is the foci 3x^2-13y^2-30x+52y=16 ?

The foci 3x^2-13y^2-30x+52y=16 is (9,2),(1,2)

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foci 3x^2-13y^2-30x+52y=16

foci

3 x^{2} - 13 y^{2} - 30 x + 52 y = 16

(9, 2), (1, 2)

Solution steps

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

Calculate Hyperbola properties

3 x^{2} - 13 y^{2} - 30 x + 52 y = 16 :

Right-left Hyperbola with

(h, k) = (5, 2), a = 13, b = 3

(5 + c, 2), (5 - c, 2)

Compute

c :

c = 13^{2} + 3^{2} : 4

(5 + 4, 2), (5 - 4, 2)

Refine

(9, 2), (1, 2)

4 x^{2} + 9 y^{2} + 3 x - 18 y^{2} + 37 = 0

9 x^{2} - 2 y^{2} = 18

\frac{x ^{2}}{49} - \frac{y ^{2}}{36} = 1

36 y^{2} - 4 x^{2} = 144

x^{2} - 4 y^{2} + 8 x + 16 y - 4 = 0

What is the foci 3x^2-13y^2-30x+52y=16 ?
The foci 3x^2-13y^2-30x+52y=16 is (9,2),(1,2)