What is the foci 9x^2+16y^2-54x+64y+1=0 ?

The foci 9x^2+16y^2-54x+64y+1=0 is (3+sqrt(7),-2),(3-sqrt(7),-2)

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foci 9x^2+16y^2-54x+64y+1=0

foci

9 x^{2} + 16 y^{2} - 54 x + 64 y + 1 = 0

(3 + 7, - 2), (3 - 7, - 2)

Solution steps

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

Calculate ellipse properties

9 x^{2} + 16 y^{2} - 54 x + 64 y + 1 = 0 :

Ellipse with center

(h, k) = (3, - 2), a = 4, b = 3

(3 + c, - 2), (3 - c, - 2)

Compute

c :

c = 4^{2} - 3^{2} : 7

(3 + 7, - 2), (3 - 7, - 2)

\frac{x ^{2}}{81} + \frac{y ^{2}}{16} = 1

9 x^{2} + 16 y^{2} + 126 x + 96 y + 441 = 0

\frac{( x - 3 ) ^{2}}{4} + \frac{( y - 2 ) ^{2}}{9} = 3

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

\frac{x ^{2}}{169} + \frac{y ^{2}}{144} = 1

What is the foci 9x^2+16y^2-54x+64y+1=0 ?
The foci 9x^2+16y^2-54x+64y+1=0 is (3+sqrt(7),-2),(3-sqrt(7),-2)