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}

(\frac{x - 5}{5})^{2} + (\frac{y + 7}{16})^{2} = 1

2 x^{2} + 4 y^{2} + 18 x + 24 y + 44 = 0

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

10 x^{2} + 40 x + 7 y^{2} + 70 y + 145 = 0

4 x^{2} + 4 y^{2} = 100 - 20 x + x^{2}

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