What is the foci-3x^2+2y^2+6x-7y=7 ?

The foci-3x^2+2y^2+6x-7y=7 is (1,(7+3sqrt(15))/4),(1,(7-3sqrt(15))/4)

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foci-3x^2+2y^2+6x-7y=7

foci

- 3 x^{2} + 2 y^{2} + 6 x - 7 y = 7

(1, \frac{7 + 3 15}{4}), (1, \frac{7 - 3 15}{4})

Solution steps

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

Calculate Hyperbola properties

- 3 x^{2} + 2 y^{2} + 6 x - 7 y = 7 :

Up-down Hyperbola with

(h, k) = (1, \frac{7}{4}), a = \frac{9}{4}, b = \frac{3 3}{2 2}

(1, \frac{7}{4} + c), (1, \frac{7}{4} - c)

Compute

c :

c = (\frac{9}{4})^{2} + (\frac{3 3}{2 2})^{2} : \frac{3 15}{4}

(1, \frac{7}{4} + \frac{3 15}{4}), (1, \frac{7}{4} - \frac{3 15}{4})

Refine

(1, \frac{7 + 3 15}{4}), (1, \frac{7 - 3 15}{4})

\frac{x ^{2}}{36} - \frac{y ^{2}}{16} = 1

x^{2} - y^{2} = 49

\frac{x ^{2}}{9} - \frac{y ^{2}}{7} = 1

\frac{x ^{2}}{100} - \frac{y ^{2}}{64} = 1

y^{2} - \frac{x ^{2}}{4} = 1

What is the foci-3x^2+2y^2+6x-7y=7 ?
The foci-3x^2+2y^2+6x-7y=7 is (1,(7+3sqrt(15))/4),(1,(7-3sqrt(15))/4)