What is the foci 16x^2-64x+9y^2=80 ?

The foci 16x^2-64x+9y^2=80 is (2,sqrt(7)),(2,-sqrt(7))

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foci 16x^2-64x+9y^2=80

foci

16 x^{2} - 64 x + 9 y^{2} = 80

(2, 7), (2, - 7)

Solution steps

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

Calculate ellipse properties

16 x^{2} - 64 x + 9 y^{2} = 80 :

Ellipse with center

(h, k) = (2, 0), b = 4, a = 3

(2, 0 + c), (2, 0 - c)

Compute

c :

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

(2, 0 + 7), (2, 0 - 7)

Refine

(2, 7), (2, - 7)

4 x^{2} + 9 y^{2} - 8 x - 32 = 0

\frac{( x - 4 ) ^{2}}{32} + \frac{( y - 3 ) ^{2}}{36} = 1

\frac{( x + 3 ) ^{2}}{21} + \frac{( y - 6 ) ^{2}}{25} = 1

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

\frac{( x - 1 ) ^{2}}{9} + \frac{( y + 4 ) ^{2}}{25} = 1

What is the foci 16x^2-64x+9y^2=80 ?
The foci 16x^2-64x+9y^2=80 is (2,sqrt(7)),(2,-sqrt(7))