What is the axis x^2+4y^2+6x+16y+21=0 ?

The axis x^2+4y^2+6x+16y+21=0 is semi-major axis a=2, semi-minor axis b=1

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axis x^2+4y^2+6x+16y+21=0

axis

x^{2} + 4 y^{2} + 6 x + 16 y + 21 = 0

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

Solution steps

x^{2} + 4 y^{2} + 6 x + 16 y + 21 = 0

Rewrite

x^{2} + 4 y^{2} + 6 x + 16 y + 21 = 0

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (- 3, - 2), a = 2, b = 1

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (- 3, - 2), a = 2, b = 1

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

\frac{x ^{2}}{36} + \frac{y ^{2}}{25} = 1

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

81 x^{2} - 1296 x + 16 y^{2} + 64 y = - 3952

4 x^{2} + 9 y^{2} + 32 x - 18 y + 37 = 0

What is the axis x^2+4y^2+6x+16y+21=0 ?
The axis x^2+4y^2+6x+16y+21=0 is semi-major axis a=2, semi-minor axis b=1