What is x^2+5y^2=20 ?

The solution to x^2+5y^2=20 is Ellipse with (h,k)=(0,0),a=2sqrt(5),b=2

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x^2+5y^2=20

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

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

Solution steps

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

Rewrite

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

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

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

\frac{1 + b + ia}{1 + b - ia} = b + ia

2 x^{2} + y^{2} + 4 x - 6 y - 12 = 0

(\frac{X}{16})^{2} + \frac{( Y + 1 ) ^{2}}{4} - 1 = 0

\frac{( x - 0 ) ^{2}}{4} + \frac{( y - 0 ) ^{2}}{16} = 1

What is x^2+5y^2=20 ?
The solution to x^2+5y^2=20 is Ellipse with (h,k)=(0,0),a=2sqrt(5),b=2