What is 2x^2+4y^2=200 ?

The solution to 2x^2+4y^2=200 is Ellipse with (h,k)=(0,0),a=10,b=5sqrt(2)

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2x^2+4y^2=200

2 x^{2} + 4 y^{2} = 200

(h, k) = (0, 0), a = 10, b = 52

Solution steps

2 x^{2} + 4 y^{2} = 200

Rewrite

2 x^{2} + 4 y^{2} = 200

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (0, 0), a = 10, b = 52

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (0, 0), a = 10, b = 52

3 x^{2} + 4 y^{2} = 1

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

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

x^{2} + \frac{y ^{2}}{5} = 1

\frac{( x + 1 ) ^{2}}{3} + \frac{( y - 1 ) ^{2}}{6} = 4

What is 2x^2+4y^2=200 ?
The solution to 2x^2+4y^2=200 is Ellipse with (h,k)=(0,0),a=10,b=5sqrt(2)