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

The axis 36x^2+5y^2-90y-495=0 is semi-major axis b=6sqrt(5), semi-minor axis a=5

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

axis

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

semi - major axis b = 65, semi - minor axis a = 5

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

x^{2} + 4 y^{2} = 46

9 x^{2} + y^{2} = 9

\frac{( x - 5 ) ^{2}}{4} + \frac{( y + 3 ) ^{2}}{16} = 1

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

\frac{x ^{2}}{36} + \frac{y ^{2}}{11} = 1

What is the axis 36x^2+5y^2-90y-495=0 ?
The axis 36x^2+5y^2-90y-495=0 is semi-major axis b=6sqrt(5), semi-minor axis a=5