What is the axis 9x^2+16y^2-54x+64y+1=0 ?

The axis 9x^2+16y^2-54x+64y+1=0 is semi-major axis a=4, semi-minor axis b=3

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axis 9x^2+16y^2-54x+64y+1=0

axis

9 x^{2} + 16 y^{2} - 54 x + 64 y + 1 = 0

semi - major axis a = 4, semi - minor axis b = 3

Solution steps

9 x^{2} + 16 y^{2} - 54 x + 64 y + 1 = 0

Rewrite

9 x^{2} + 16 y^{2} - 54 x + 64 y + 1 = 0

in the form of the standard ellipse equation

\frac{( x - 3 ) ^{2}}{4 ^{2}} + \frac{( y - ( - 2 ) ) ^{2}}{3 ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (3, - 2), a = 4, b = 3

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (3, - 2), a = 4, b = 3

\frac{( x - 1 ) ^{2}}{9} + \frac{( y + 5 ) ^{2}}{16} = 1

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

25 x^{2} + 16 y^{2} = 400

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

9 x^{2} + 4 y^{2} + 18 x - 8 y - 131 = 0

What is the axis 9x^2+16y^2-54x+64y+1=0 ?
The axis 9x^2+16y^2-54x+64y+1=0 is semi-major axis a=4, semi-minor axis b=3