What is the axis 3x^2+7y^2-12x-28y+19=0 ?

The axis 3x^2+7y^2-12x-28y+19=0 is semi-major axis a=sqrt(7), semi-minor axis b=sqrt(3)

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axis 3x^2+7y^2-12x-28y+19=0

axis

3 x^{2} + 7 y^{2} - 12 x - 28 y + 19 = 0

semi - major axis a = 7, semi - minor axis b = 3

Solution steps

3 x^{2} + 7 y^{2} - 12 x - 28 y + 19 = 0

Rewrite

3 x^{2} + 7 y^{2} - 12 x - 28 y + 19 = 0

in the form of the standard ellipse equation

\frac{( x - 2 ) ^{2}}{( 7 ) ^{2}} + \frac{( y - 2 ) ^{2}}{( 3 ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (2, 2), a = 7, b = 3

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (2, 2), a = 7, b = 3

x^{2} + y^{2} - 6 y = 0

\frac{x ^{2}}{20} + \frac{y ^{2}}{4} = 1

25 x^{2} + 4 y^{2} + 50 x - 16 y - 59 = 0

9 x^{2} + 4 y^{2} + 54 x - 8 y + 49 = 0

x^{2} + 2 y^{2} - 2 x + 8 y + 5 = 0

What is the axis 3x^2+7y^2-12x-28y+19=0 ?
The axis 3x^2+7y^2-12x-28y+19=0 is semi-major axis a=sqrt(7), semi-minor axis b=sqrt(3)