What is the axis x^2+4y^2=10 ?

The axis x^2+4y^2=10 is semi-major axis a=sqrt(10), semi-minor axis b=sqrt(5/2)

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axis x^2+4y^2=10

axis

x^{2} + 4 y^{2} = 10

semi - major axis a = 10, semi - minor axis b = \frac{5}{2}

Solution steps

x^{2} + 4 y^{2} = 10

Rewrite

x^{2} + 4 y^{2} = 10

in the form of the standard ellipse equation

\frac{( x - 0 ) ^{2}}{( 10 ) ^{2}} + \frac{( y - 0 ) ^{2}}{( \frac{5}{2} ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (0, 0), a = 10, b = \frac{5}{2}

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (0, 0), a = 10, b = \frac{5}{2}

\frac{( x - 5 ) ^{2}}{25} + \frac{( y - 4 ) ^{2}}{4} = 1

\frac{x ^{2}}{49} + \frac{y ^{2}}{16} = 1

x^{2} + y^{2} - 4 x + 6 y = 3

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

x^{2} + 2 y^{2} + 2 x - 4 y - 1 = 0

What is the axis x^2+4y^2=10 ?
The axis x^2+4y^2=10 is semi-major axis a=sqrt(10), semi-minor axis b=sqrt(5/2)