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

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

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axis 9x^2+4y^2=36

axis

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

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

Solution steps

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

Rewrite

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

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (0, 0), a = 2, b = 3

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (0, 0), b = 3, a = 2

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

16 x^{2} + 25 y^{2} = 400

\frac{x ^{2}}{144} + \frac{y ^{2}}{169} = 1

\frac{x ^{2}}{25} + \frac{y ^{2}}{36} = 1

9 x^{2} + 16 y^{2} = 144

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