What is the axis 3x^2+7y^2=63 ?

The axis 3x^2+7y^2=63 is semi-major axis a=sqrt(21), semi-minor axis b=3

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axis 3x^2+7y^2=63

axis

3 x^{2} + 7 y^{2} = 63

semi - major axis a = 21, semi - minor axis b = 3

Solution steps

3 x^{2} + 7 y^{2} = 63

Rewrite

3 x^{2} + 7 y^{2} = 63

in the form of the standard ellipse equation

\frac{( x - 0 ) ^{2}}{( 21 ) ^{2}} + \frac{( y - 0 ) ^{2}}{3 ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (0, 0), a = 21, b = 3

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (0, 0), a = 21, b = 3

x^{2} + 4 y^{2} = 25

4 x^{2} + 9 y^{2} - 8 x - 36 y + 4 = 0

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

3 x^{2} + 4 y^{2} + 27 x - 16 y + 48 = 0

\frac{( x - 4 ) ^{2}}{81} + \frac{( y + 9 ) ^{2}}{4} = 1

What is the axis 3x^2+7y^2=63 ?
The axis 3x^2+7y^2=63 is semi-major axis a=sqrt(21), semi-minor axis b=3