What is x/(x^2+y^2)=-3/4 ?

The solution to x/(x^2+y^2)=-3/4 is Ellipse with (h,k)=(-2/3 ,0),a= 2/3 ,b= 2/3

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x/(x^2+y^2)=-3/4

\frac{x}{x ^{2} + y ^{2}} = - \frac{3}{4}

(h, k) = (- \frac{2}{3}, 0), a = \frac{2}{3}, b = \frac{2}{3}

Solution steps

\frac{x}{x ^{2} + y ^{2}} = - \frac{3}{4}

Rewrite

\frac{x}{x ^{2} + y ^{2}} = - \frac{3}{4}

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (- \frac{2}{3}, 0), a = \frac{2}{3}, b = \frac{2}{3}

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (- \frac{2}{3}, 0), b = \frac{2}{3}, a = \frac{2}{3}

\frac{( x + 1 ) ^{2}}{\frac{27}{4}} + \frac{( y - 4 ) ^{2}}{9} = 1

9 - x^{2} - 9 y^{2} = 0

\frac{( x - 5 ) ^{2}}{25} + \frac{( y - 3 ) ^{2}}{9} = 1

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

4 x^{2} + 9 y^{2} - 8 x - 54 y - 5 = 0

What is x/(x^2+y^2)=-3/4 ?
The solution to x/(x^2+y^2)=-3/4 is Ellipse with (h,k)=(-2/3 ,0),a= 2/3 ,b= 2/3