What is the foci 6x^2+9y^2-18y-45=0 ?

The foci 6x^2+9y^2-18y-45=0 is (sqrt(3),1),(-sqrt(3),1)

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foci 6x^2+9y^2-18y-45=0

foci

6 x^{2} + 9 y^{2} - 18 y - 45 = 0

(3, 1), (- 3, 1)

Solution steps

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

Calculate ellipse properties

6 x^{2} + 9 y^{2} - 18 y - 45 = 0 :

Ellipse with center

(h, k) = (0, 1), a = 3, b = 6

(0 + c, 1), (0 - c, 1)

Compute

c :

c = 3^{2} - 6^{2} : 3

(0 + 3, 1), (0 - 3, 1)

Refine

(3, 1), (- 3, 1)

\frac{( x - 1 ) ^{2}}{9} + \frac{( y + 2 ) ^{2}}{5} = 1

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

4 x^{2} + 9 y^{2} + 16 x - 90 y + 205 = 0

9 x^{2} + 4 y^{2} - 18 x - 16 y - 11 = 0

\frac{( x - 1 ) ^{2}}{36} + \frac{( y - 2 ) ^{2}}{115} = 3

What is the foci 6x^2+9y^2-18y-45=0 ?
The foci 6x^2+9y^2-18y-45=0 is (sqrt(3),1),(-sqrt(3),1)