What is the axis 4x^2+y^2+16x+4y+4=0 ?

The axis 4x^2+y^2+16x+4y+4=0 is semi-major axis b=4, semi-minor axis a=2

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axis 4x^2+y^2+16x+4y+4=0

axis

4 x^{2} + y^{2} + 16 x + 4 y + 4 = 0

semi - major axis b = 4, semi - minor axis a = 2

Solution steps

4 x^{2} + y^{2} + 16 x + 4 y + 4 = 0

Rewrite

4 x^{2} + y^{2} + 16 x + 4 y + 4 = 0

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

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

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

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

5 x^{2} + 2 y^{2} = 50

\frac{( x - 2 ) ^{2}}{9} + \frac{( y - 3 ) ^{2}}{16} = 1

\frac{( x - 5 ) ^{2}}{36} + \frac{( y - 1 ) ^{2}}{16} = 1

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

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

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