What is the foci 9x^2+49y^2+18x+294y-9=0 ?

The foci 9x^2+49y^2+18x+294y-9=0 is ((-7+2sqrt(510))/7 ,-3),((-7-2sqrt(510))/7 ,-3)

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foci 9x^2+49y^2+18x+294y-9=0

foci

9 x^{2} + 49 y^{2} + 18 x + 294 y - 9 = 0

(\frac{- 7 + 2 510}{7}, - 3), (\frac{- 7 - 2 510}{7}, - 3)

Solution steps

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

Calculate ellipse properties

9 x^{2} + 49 y^{2} + 18 x + 294 y - 9 = 0 :

Ellipse with center

(h, k) = (- 1, - 3), a = 51, b = \frac{3 51}{7}

(- 1 + c, - 3), (- 1 - c, - 3)

Compute

c :

c = 51^{2} - (\frac{3 51}{7})^{2} : \frac{2 510}{7}

(- 1 + \frac{2 510}{7}, - 3), (- 1 - \frac{2 510}{7}, - 3)

Refine

(\frac{- 7 + 2 510}{7}, - 3), (\frac{- 7 - 2 510}{7}, - 3)

9 x^{2} + 7 y^{2} - 63 = 0

16 x^{2} + 64 y^{2} = 128

(\frac{x ^{2}}{4}) + y^{2} = 1

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

\frac{( x - 1 ) ^{2}}{5} + \frac{( y - 3 ) ^{2}}{4} = 1

What is the foci 9x^2+49y^2+18x+294y-9=0 ?
The foci 9x^2+49y^2+18x+294y-9=0 is ((-7+2sqrt(510))/7 ,-3),((-7-2sqrt(510))/7 ,-3)