What is (x^2)/(200)+(y^2)/(50)=1 ?

The solution to (x^2)/(200)+(y^2)/(50)=1 is Ellipse with (h,k)=(0,0),a=10sqrt(2),b=5sqrt(2)

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(x^2)/(200)+(y^2)/(50)=1

\frac{x ^{2}}{200} + \frac{y ^{2}}{50} = 1

(h, k) = (0, 0), a = 102, b = 52

Solution steps

\frac{x ^{2}}{200} + \frac{y ^{2}}{50} = 1

Rewrite

\frac{x ^{2}}{200} + \frac{y ^{2}}{50} = 1

in the form of the standard ellipse equation

\frac{( x - 0 ) ^{2}}{( 10 2 ) ^{2}} + \frac{( y - 0 ) ^{2}}{( 5 2 ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (0, 0), a = 102, b = 52

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (0, 0), a = 102, b = 52

\frac{x ^{2}}{81} + \frac{y ^{2}}{144} = 1

4 x^{2} + 9 y^{2} = 1 - x - y

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

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

- x^{2} - \frac{y ^{2}}{49} = 1

What is (x^2)/(200)+(y^2)/(50)=1 ?
The solution to (x^2)/(200)+(y^2)/(50)=1 is Ellipse with (h,k)=(0,0),a=10sqrt(2),b=5sqrt(2)