What is the foci x^2-4x+9y^2+54y+4=0 ?

The foci x^2-4x+9y^2+54y+4=0 is (2+6sqrt(2),-3),(2-6sqrt(2),-3)

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foci x^2-4x+9y^2+54y+4=0

foci

x^{2} - 4 x + 9 y^{2} + 54 y + 4 = 0

(2 + 62, - 3), (2 - 62, - 3)

Solution steps

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

Calculate ellipse properties

x^{2} - 4 x + 9 y^{2} + 54 y + 4 = 0 :

Ellipse with center

(h, k) = (2, - 3), a = 9, b = 3

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

Compute

c :

c = 9^{2} - 3^{2} : 62

(2 + 62, - 3), (2 - 62, - 3)

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

x^{2} + 5 y^{2} - 2 x + 10 y = - 1

(\frac{x}{8})^{2} + (\frac{y}{6})^{2} = 1

\frac{x ^{2}}{484} + \frac{y ^{2}}{289} = 1

x^{2} + 9 y^{2} + 2 x - 54 y + 46 = 0

What is the foci x^2-4x+9y^2+54y+4=0 ?
The foci x^2-4x+9y^2+54y+4=0 is (2+6sqrt(2),-3),(2-6sqrt(2),-3)