What is 20x^2+25y^2=400 ?

The solution to 20x^2+25y^2=400 is Ellipse with (h,k)=(0,0),a=2sqrt(5),b=4

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20x^2+25y^2=400

20 x^{2} + 25 y^{2} = 400

(h, k) = (0, 0), a = 25, b = 4

Solution steps

20 x^{2} + 25 y^{2} = 400

Rewrite

20 x^{2} + 25 y^{2} = 400

in the form of the standard ellipse equation

\frac{( x - 0 ) ^{2}}{( 2 5 ) ^{2}} + \frac{( y - 0 ) ^{2}}{4 ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (0, 0), a = 25, b = 4

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (0, 0), a = 25, b = 4

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

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

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

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

\frac{( x - 0 ) ^{2}}{25} + \frac{( y - 0 ) ^{2}}{2.25} = 1

What is 20x^2+25y^2=400 ?
The solution to 20x^2+25y^2=400 is Ellipse with (h,k)=(0,0),a=2sqrt(5),b=4