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

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

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

axis

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

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

Solution steps

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

Rewrite

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

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

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

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

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

x^{2} + \frac{y ^{2}}{49} = 1

\frac{( x + 6 ) ^{2}}{18} + \frac{( y + 3 ) ^{2}}{9} = 1

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

3 x^{2} + 7 y^{2} - 12 x - 28 y + 19 = 0

x^{2} + y^{2} - 6 y = 0

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