What is x/((x^2+y^2))= 3/2 ?

The solution to x/((x^2+y^2))= 3/2 is Ellipse with (h,k)=(1/3 ,0),a= 1/3 ,b= 1/3

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x/((x^2+y^2))= 3/2

\frac{x}{( x ^{2} + y ^{2} )} = \frac{3}{2}

(h, k) = (\frac{1}{3}, 0), a = \frac{1}{3}, b = \frac{1}{3}

Solution steps

\frac{x}{x ^{2} + y ^{2}} = \frac{3}{2}

Rewrite

\frac{x}{x ^{2} + y ^{2}} = \frac{3}{2}

in the form of the standard ellipse equation

\frac{( x - \frac{1}{3} ) ^{2}}{( \frac{1}{3} ) ^{2}} + \frac{( y - 0 ) ^{2}}{( \frac{1}{3} ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (\frac{1}{3}, 0), a = \frac{1}{3}, b = \frac{1}{3}

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (\frac{1}{3}, 0), b = \frac{1}{3}, a = \frac{1}{3}

\frac{( x + 2 ) ^{2}}{16} + \frac{( y - 2 ) ^{2}}{12} = 1

2 x^{2} + y^{2} + 10 x + 12 y = - 12

\frac{x ^{2}}{15} + \frac{y ^{2}}{4} = 1

5 x^{2} + y^{2} = 25

4 (x - 5)^{2} + 3 (y - 5)^{2} = 192

What is x/((x^2+y^2))= 3/2 ?
The solution to x/((x^2+y^2))= 3/2 is Ellipse with (h,k)=(1/3 ,0),a= 1/3 ,b= 1/3