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 + 4 ) ^{2}}{4} + \frac{( y + 3 ) ^{2}}{9} = 1

2 x^{2} + 4 y^{2} + 8 x + 9 y - 3 = 0

36 x^{2} + 4 y^{2} + 360 x - 32 y + 820 = 0

\frac{( x - 1 ) ^{2}}{100} + \frac{( y - 2 ) ^{2}}{36} = 1

\frac{( x + 6 ) ^{2}}{4} + \frac{( y + 6 ) ^{2}}{25} = 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)