What is the axis 5x^2+2y^2=10 ?

The axis 5x^2+2y^2=10 is semi-major axis b=sqrt(5), semi-minor axis a=sqrt(2)

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axis 5x^2+2y^2=10

axis

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

semi - major axis b = 5, semi - minor axis a = 2

Solution steps

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

Rewrite

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

in the form of the standard ellipse equation

\frac{( x - 0 ) ^{2}}{( 2 ) ^{2}} + \frac{( y - 0 ) ^{2}}{( 5 ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (0, 0), a = 2, b = 5

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (0, 0), b = 5, a = 2

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

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

4 x^{2} + 2 y^{2} + 2 x - 8 y + 7 = 0

\frac{( x + 4 ) ^{2}}{9} + \frac{( y - 6 ) ^{2}}{25} = 1

6.25 x^{2} + 16 y^{2} - 12.5 x + 64 y - 29.75 = 0

What is the axis 5x^2+2y^2=10 ?
The axis 5x^2+2y^2=10 is semi-major axis b=sqrt(5), semi-minor axis a=sqrt(2)