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

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

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

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

(h, k) = (\frac{1}{2}, 0), a = \frac{1}{2}, b = \frac{1}{2}

Solution steps

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

Rewrite

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

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (\frac{1}{2}, 0), a = \frac{1}{2}, b = \frac{1}{2}

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (\frac{1}{2}, 0), b = \frac{1}{2}, a = \frac{1}{2}

2 x^{2} + 3 y^{2} + 12 x - 24 y + 60 = 0

\frac{x ^{2}}{4} + \frac{( y - 1 ) ^{2}}{9} < 1

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

4 x^{2} + 25 y^{2} - 24 x + 250 y + 561 = 0

x^{2} + 9 y^{2} - 18 y = 0

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