What is the center 36x^2+5y^2-90y-495=0 ?

The center 36x^2+5y^2-90y-495=0 is (0,9)

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center 36x^2+5y^2-90y-495=0

center

36 x^{2} + 5 y^{2} - 90 y - 495 = 0

(0, 9)

Solution steps

36 x^{2} + 5 y^{2} - 90 y - 495 = 0

Rewrite

36 x^{2} + 5 y^{2} - 90 y - 495 = 0

in the form of the standard ellipse equation

\frac{( x - 0 ) ^{2}}{5 ^{2}} + \frac{( y - 9 ) ^{2}}{( 6 5 ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (0, 9), a = 5, b = 65

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (0, 9), b = 65, a = 5

And the center is:

(0, 9)

x^{2} + 4 y^{2} = 36

\frac{( x + 1 ) ^{2}}{16} + \frac{( y - 2 ) ^{2}}{25} = 1

4 x^{2} + y^{2} + 12 x + 6 y + 5 = 0

x^{2} + 5 y^{2} - 4 x + 20 y = - 19

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

What is the center 36x^2+5y^2-90y-495=0 ?
The center 36x^2+5y^2-90y-495=0 is (0,9)