What is the foci 9x^2-54x+4y^2=-45 ?

The foci 9x^2-54x+4y^2=-45 is (3,sqrt(5)),(3,-sqrt(5))

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foci 9x^2-54x+4y^2=-45

foci

9 x^{2} - 54 x + 4 y^{2} = - 45

(3, 5), (3, - 5)

Solution steps

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

Calculate ellipse properties

9 x^{2} - 54 x + 4 y^{2} = - 45 :

Ellipse with center

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

(3, 0 + c), (3, 0 - c)

Compute

c :

c = 3^{2} - 2^{2} : 5

(3, 0 + 5), (3, 0 - 5)

Refine

(3, 5), (3, - 5)

\frac{( x + 2 ) ^{2}}{25} + \frac{( y - 1 ) ^{2}}{144} = 1

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

25 x^{2} + 9 y^{2} - 100 x + 18 y - 116 = 0

\frac{x ^{2}}{81} + \frac{y ^{2}}{49} = 1

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

What is the foci 9x^2-54x+4y^2=-45 ?
The foci 9x^2-54x+4y^2=-45 is (3,sqrt(5)),(3,-sqrt(5))