What is the axis 9x^2+4y^2-18x+8y-23=0 ?

The axis 9x^2+4y^2-18x+8y-23=0 is semi-major axis b=3, semi-minor axis a=2

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axis 9x^2+4y^2-18x+8y-23=0

axis

9 x^{2} + 4 y^{2} - 18 x + 8 y - 23 = 0

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

Solution steps

9 x^{2} + 4 y^{2} - 18 x + 8 y - 23 = 0

Rewrite

9 x^{2} + 4 y^{2} - 18 x + 8 y - 23 = 0

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

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

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

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

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

4 x^{2} + 9 y^{2} - 8 x + 90 y + 193 = 0

\frac{x ^{2}}{49} + \frac{y ^{2}}{169} = 1

5 x^{2} + 7 y^{2} = 35

x^{2} + \frac{( y - 6 ) ^{2}}{16} = 1

What is the axis 9x^2+4y^2-18x+8y-23=0 ?
The axis 9x^2+4y^2-18x+8y-23=0 is semi-major axis b=3, semi-minor axis a=2