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

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

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

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

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

Solution steps

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

Rewrite

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

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 ^{2}}{3. 5 ^{2}} + \frac{y ^{2}}{2. 5 ^{2}} = 1

12 x^{2} + y^{2} = 24

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

36 x^{2} + 16 y^{2} = 576

9 x^{2} + 18 x + 16 y^{2} - 96 y + 9 = 0

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