What is the axis 9x^2+4y^2-18x+16y-11=0 ?

The axis 9x^2+4y^2-18x+16y-11=0 is semi-major axis b=3, semi-minor axis a=2

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

axis

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

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

Solution steps

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

Rewrite

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

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

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

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

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

\frac{x ^{2}}{4} + \frac{y ^{2}}{9} = 1

\frac{x ^{2}}{25} + \frac{y ^{2}}{4} = 1

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

\frac{x ^{2}}{81} + \frac{y ^{2}}{16} = 1

\frac{( x - 2 ) ^{2}}{64} + \frac{( y + 4 ) ^{2}}{16} = 1

What is the axis 9x^2+4y^2-18x+16y-11=0 ?
The axis 9x^2+4y^2-18x+16y-11=0 is semi-major axis b=3, semi-minor axis a=2