What is the axis x^2+4y^2-6x+8y+9=0 ?

The axis x^2+4y^2-6x+8y+9=0 is semi-major axis a=2, semi-minor axis b=1

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axis x^2+4y^2-6x+8y+9=0

axis

x^{2} + 4 y^{2} - 6 x + 8 y + 9 = 0

semi - major axis a = 2, semi - minor axis b = 1

Solution steps

x^{2} + 4 y^{2} - 6 x + 8 y + 9 = 0

Rewrite

x^{2} + 4 y^{2} - 6 x + 8 y + 9 = 0

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (3, - 1), a = 2, b = 1

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (3, - 1), a = 2, b = 1

2 x^{2} + y^{2} = 50

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

\frac{( x + 4 ) ^{2}}{9} + \frac{( y - 6 ) ^{2}}{25} = 1

6.25 x^{2} + 16 y^{2} - 12.5 x + 64 y - 29.75 = 0

4 x^{2} + 49 y^{2} = 196

What is the axis x^2+4y^2-6x+8y+9=0 ?
The axis x^2+4y^2-6x+8y+9=0 is semi-major axis a=2, semi-minor axis b=1