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

The axis 4x^2+y^2+8x-4y+4=0 is semi-major axis b=2, semi-minor axis a=1

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axis 4x^2+y^2+8x-4y+4=0

axis

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

semi - major axis b = 2, semi - minor axis a = 1

Solution steps

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

Rewrite

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

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

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

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

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

4 x^{2} + 9 y^{2} - 16 x + 18 y = 11

x^{2} + 4 y^{2} = 16

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

\frac{x ^{2}}{100} + \frac{y ^{2}}{64} = 1

16 x^{2} + 25 y^{2} + 32 x - 384 = 0

What is the axis 4x^2+y^2+8x-4y+4=0 ?
The axis 4x^2+y^2+8x-4y+4=0 is semi-major axis b=2, semi-minor axis a=1