What is the axis x^2+y^2-4x+6y=3 ?

The axis x^2+y^2-4x+6y=3 is semi-major axis b=4, semi-minor axis a=4

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axis x^2+y^2-4x+6y=3

axis

x^{2} + y^{2} - 4 x + 6 y = 3

semi - major axis b = 4, semi - minor axis a = 4

Solution steps

x^{2} + y^{2} - 4 x + 6 y = 3

Rewrite

x^{2} + y^{2} - 4 x + 6 y = 3

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (2, - 3), a = 4, b = 4

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (2, - 3), b = 4, a = 4

\frac{x ^{2}}{4} + y^{2} = 1

x^{2} + 2 y^{2} + 2 x - 4 y - 1 = 0

27 x^{2} + 48 y^{2} - 54 x - 192 y - 213 = 0

4 x^{2} + 25 y^{2} + 32 x - 250 y + 589 = 0

4 x^{2} + y^{2} = 1

What is the axis x^2+y^2-4x+6y=3 ?
The axis x^2+y^2-4x+6y=3 is semi-major axis b=4, semi-minor axis a=4