What is the axis (x^2}{20}+\frac{y^2)/4 =1 ?

The axis (x^2}{20}+\frac{y^2)/4 =1 is semi-major axis a=2sqrt(5), semi-minor axis b=2

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axis (x^2}{20}+\frac{y^2)/4 =1

axis

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

semi - major axis a = 25, semi - minor axis b = 2

Solution steps

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

Rewrite

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

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (0, 0), a = 25, b = 2

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (0, 0), a = 25, b = 2

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

4 x^{2} + 8 y^{2} - 16 \cdot + 32 y + 32 = 0

16 x^{2} + 9 y^{2} - 128 x - 18 y + 121 = 0

What is the axis (x^2}{20}+\frac{y^2)/4 =1 ?
The axis (x^2}{20}+\frac{y^2)/4 =1 is semi-major axis a=2sqrt(5), semi-minor axis b=2