What is the axis 9x^2+4y^2+36x-24y+36=0 ?

The axis 9x^2+4y^2+36x-24y+36=0 is semi-major axis b=3, semi-minor axis a=2

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axis 9x^2+4y^2+36x-24y+36=0

axis

9 x^{2} + 4 y^{2} + 36 x - 24 y + 36 = 0

semi - major axis b = 3, semi - minor axis a = 2

Solution steps

9 x^{2} + 4 y^{2} + 36 x - 24 y + 36 = 0

Rewrite

9 x^{2} + 4 y^{2} + 36 x - 24 y + 36 = 0

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

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

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (- 2, 3), b = 3, a = 2

9 x^{2} + 25 y^{2} - 36 x - 50 y + 60 = 0

25 x^{2} + 4 y^{2} = 100

36 x^{2} + 288 x + 64 y^{2} - 256 y = 1472

\frac{x ^{2}}{100} + \frac{y ^{2}}{36} = 1

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

What is the axis 9x^2+4y^2+36x-24y+36=0 ?
The axis 9x^2+4y^2+36x-24y+36=0 is semi-major axis b=3, semi-minor axis a=2