What is the axis 9x^2+4y^2+54x-8y+49=0 ?

The axis 9x^2+4y^2+54x-8y+49=0 is semi-major axis b=3, semi-minor axis a=2

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axis 9x^2+4y^2+54x-8y+49=0

axis

9 x^{2} + 4 y^{2} + 54 x - 8 y + 49 = 0

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

Solution steps

9 x^{2} + 4 y^{2} + 54 x - 8 y + 49 = 0

Rewrite

9 x^{2} + 4 y^{2} + 54 x - 8 y + 49 = 0

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

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

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

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

x^{2} + 2 y^{2} - 2 x + 8 y + 5 = 0

4 x^{2} + 8 y^{2} - 16 \cdot + 32 y + 32 = 0

16 x^{2} + 9 y^{2} - 128 x - 18 y + 121 = 0

\frac{( x - 30 ) ^{2}}{4 0 ^{2}} + \frac{y ^{2}}{2 ^{2}} = 1

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

What is the axis 9x^2+4y^2+54x-8y+49=0 ?
The axis 9x^2+4y^2+54x-8y+49=0 is semi-major axis b=3, semi-minor axis a=2