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

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

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

center

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

(0, 1)

Solution steps

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

Rewrite

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

in the form of the standard ellipse equation

\frac{( x - 0 ) ^{2}}{3 ^{2}} + \frac{( y - 1 ) ^{2}}{( 6 ) ^{2}} = 1

Therefore ellipse properties are:

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

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

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

And the center is:

(0, 1)

\frac{x ^{2}}{36} + \frac{y ^{2}}{16} = 1

9 x^{2} - 36 x + 4 y^{2} = 0

3 (x + 1)^{2} + (y - 1)^{2} = 6

4 x^{2} + 2 y^{2} + 2 x - 8 y + 7 = 0

\frac{( x - 3 ) ^{2}}{25} + \frac{( y + 2 ) ^{2}}{81} = 1