What is 4x^2+5y^2=20 ?

The solution to 4x^2+5y^2=20 is Ellipse with (h,k)=(0,0),a=sqrt(5),b=2

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4x^2+5y^2=20

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

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

Solution steps

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

Rewrite

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

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

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

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

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

\frac{( x - 2 ) ^{2}}{36} + \frac{( y - 3 ) ^{2}}{81} = 1

36 x^{2} + 16 y^{2} - 180 x + 96 y - 207 = 0

x^{2} + 3 y^{2} = 9

12 x^{2} + 16 y^{2} - 120 x + 64 y + 172 = 0

16 x^{2} + 9 y^{2} - 64 x - 54 y + 1 = 0

What is 4x^2+5y^2=20 ?
The solution to 4x^2+5y^2=20 is Ellipse with (h,k)=(0,0),a=sqrt(5),b=2