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}

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x^{2} + 4 y^{2} - 2.71 = 0

\frac{( x - 5 ) ^{2}}{144} + \frac{( y + 2 ) ^{2}}{169} = 1

4 y^{(2)} + 2 x^{(2)} - 4 y - 8 x - 15 = 0

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

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