What is the axis 16x^2+y^2-64x+8y+16=0 ?

The axis 16x^2+y^2-64x+8y+16=0 is semi-major axis b=8, semi-minor axis a=2

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axis 16x^2+y^2-64x+8y+16=0

axis

16 x^{2} + y^{2} - 64 x + 8 y + 16 = 0

semi - major axis b = 8, semi - minor axis a = 2

Solution steps

16 x^{2} + y^{2} - 64 x + 8 y + 16 = 0

Rewrite

16 x^{2} + y^{2} - 64 x + 8 y + 16 = 0

in the form of the standard ellipse equation

\frac{( x - 2 ) ^{2}}{2 ^{2}} + \frac{( y - ( - 4 ) ) ^{2}}{8 ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (2, - 4), a = 2, b = 8

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (2, - 4), b = 8, a = 2

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

\frac{( x - 8 ) ^{2}}{49} + \frac{( y + 1 ) ^{2}}{100} = 1

\frac{x ^{2}}{36} + \frac{y ^{2}}{16} = 1

\frac{x ^{2}}{16} + (y - 4)^{2} = 1

49 x^{2} + 64 y^{2} = 25

What is the axis 16x^2+y^2-64x+8y+16=0 ?
The axis 16x^2+y^2-64x+8y+16=0 is semi-major axis b=8, semi-minor axis a=2