What is the axis 4x^2+9y^2-64x+54y+301=0 ?

The axis 4x^2+9y^2-64x+54y+301=0 is semi-major axis a=3, semi-minor axis b=2

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axis 4x^2+9y^2-64x+54y+301=0

axis

4 x^{2} + 9 y^{2} - 64 x + 54 y + 301 = 0

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

Solution steps

4 x^{2} + 9 y^{2} - 64 x + 54 y + 301 = 0

Rewrite

4 x^{2} + 9 y^{2} - 64 x + 54 y + 301 = 0

in the form of the standard ellipse equation

\frac{( x - 8 ) ^{2}}{3 ^{2}} + \frac{( y - ( - 3 ) ) ^{2}}{2 ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (8, - 3), a = 3, b = 2

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (8, - 3), a = 3, b = 2

x^{2} + 4 y^{2} = 10

\frac{( x - 5 ) ^{2}}{25} + \frac{( y - 4 ) ^{2}}{4} = 1

\frac{x ^{2}}{49} + \frac{y ^{2}}{16} = 1

x^{2} + y^{2} - 4 x + 6 y = 3

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

What is the axis 4x^2+9y^2-64x+54y+301=0 ?
The axis 4x^2+9y^2-64x+54y+301=0 is semi-major axis a=3, semi-minor axis b=2