What is the axis 5x^2+20y^2=50 ?

The axis 5x^2+20y^2=50 is semi-major axis a=sqrt(10), semi-minor axis b=sqrt(5/2)

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axis 5x^2+20y^2=50

axis

5 x^{2} + 20 y^{2} = 50

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

Solution steps

5 x^{2} + 20 y^{2} = 50

Rewrite

5 x^{2} + 20 y^{2} = 50

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 ^{2}}{3} + \frac{y ^{2}}{9} = 1

16 x^{2} + 25 y^{2} + 32 x - 150 y - 159 = 0

\frac{( x + 3 ) ^{2}}{25} + \frac{( y - 8 ) ^{2}}{16} = 1

4 x^{2} + 9 y^{2} - 16 x + 18 y - 11 = 0

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

What is the axis 5x^2+20y^2=50 ?
The axis 5x^2+20y^2=50 is semi-major axis a=sqrt(10), semi-minor axis b=sqrt(5/2)