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}}{\frac{81}{4}} + \frac{y ^{2}}{\frac{26}{16}} = 1

y^{2} = 1 - \frac{x ^{2}}{a ^{2}}

25 x^{2} + 9 y^{2} + 200 x - 36 y + 211 = 0

4 x^{2} + 9 y^{2} - 8 x + 36 y + 4 = 0

- 5 x^{2} - 6 y^{2} = 1

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