What is the axis 3x^2+y^2+2x-6y=3 ?

The axis 3x^2+y^2+2x-6y=3 is semi-major axis b=sqrt(37/3), semi-minor axis a=(sqrt(37))/3

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axis 3x^2+y^2+2x-6y=3

axis

3 x^{2} + y^{2} + 2 x - 6 y = 3

semi - major axis b = \frac{37}{3}, semi - minor axis a = \frac{37}{3}

Solution steps

3 x^{2} + y^{2} + 2 x - 6 y = 3

Rewrite

3 x^{2} + y^{2} + 2 x - 6 y = 3

in the form of the standard ellipse equation

\frac{( x - ( - \frac{1}{3} ) ) ^{2}}{( \frac{37}{3} ) ^{2}} + \frac{( y - 3 ) ^{2}}{( \frac{37}{3} ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (- \frac{1}{3}, 3), a = \frac{37}{3}, b = \frac{37}{3}

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (- \frac{1}{3}, 3), b = \frac{37}{3}, a = \frac{37}{3}

\frac{( x - 8 ) ^{2}}{49} + \frac{( y + 1 ) ^{2}}{100} = 1

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

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

49 x^{2} + 64 y^{2} = 25

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

What is the axis 3x^2+y^2+2x-6y=3 ?
The axis 3x^2+y^2+2x-6y=3 is semi-major axis b=sqrt(37/3), semi-minor axis a=(sqrt(37))/3