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

The solution to x/(x^2+y^2)=2 is Ellipse with (h,k)=(1/4 ,0),a= 1/4 ,b= 1/4

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x/(x^2+y^2)=2

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

(h, k) = (\frac{1}{4}, 0), a = \frac{1}{4}, b = \frac{1}{4}

Solution steps

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

Rewrite

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

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (\frac{1}{4}, 0), a = \frac{1}{4}, b = \frac{1}{4}

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (\frac{1}{4}, 0), b = \frac{1}{4}, a = \frac{1}{4}

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

\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

What is x/(x^2+y^2)=2 ?
The solution to x/(x^2+y^2)=2 is Ellipse with (h,k)=(1/4 ,0),a= 1/4 ,b= 1/4