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

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

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

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

(h, k) = (1, 0), a = 1, b = 1

Solution steps

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

Rewrite

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

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (1, 0), a = 1, b = 1

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (1, 0), b = 1, a = 1

\frac{( x + 1 ) ^{2}}{5} + \frac{( y - 3 ) ^{2}}{9} = 1

16 - 2 x^{2} - y^{2} > 0

x^{2} + 2 y^{2} + 4 x - 8 y - 6 = 0

8 x^{2} + 2 y^{2} - 32 = 0

\frac{( x - 3 ) ^{2}}{5} + \frac{( y + 1 ) ^{2}}{9} = 1

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