What is the axis 3x^2+12x+4y^2-40y+100=0 ?

The axis 3x^2+12x+4y^2-40y+100=0 is semi-major axis a=2, semi-minor axis b=sqrt(3)

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axis 3x^2+12x+4y^2-40y+100=0

axis

3 x^{2} + 12 x + 4 y^{2} - 40 y + 100 = 0

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

Solution steps

3 x^{2} + 12 x + 4 y^{2} - 40 y + 100 = 0

Rewrite

3 x^{2} + 12 x + 4 y^{2} - 40 y + 100 = 0

in the form of the standard ellipse equation

\frac{( x - ( - 2 ) ) ^{2}}{2 ^{2}} + \frac{( y - 5 ) ^{2}}{( 3 ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (- 2, 5), a = 2, b = 3

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (- 2, 5), a = 2, b = 3

\frac{( x - 3 ) ^{2}}{49} + \frac{( y + 6 ) ^{2}}{100} = 1

2 x^{2} + 7 y^{2} = 14

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

x^{2} + 4 y^{2} - 6 x + 8 y + 9 = 0

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

What is the axis 3x^2+12x+4y^2-40y+100=0 ?
The axis 3x^2+12x+4y^2-40y+100=0 is semi-major axis a=2, semi-minor axis b=sqrt(3)