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

The solution to (4x)/(x^2+y^2)=-2 is Ellipse with (h,k)=(-1,0),a=1,b=1

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

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

(h, k) = (- 1, 0), a = 1, b = 1

Solution steps

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

Rewrite

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

y^{2} + 4 x^{2} + 24 x + 16 y = - 84

\frac{y ^{2}}{10} + \frac{x ^{2}}{6} = 1

x^{2} - 8 x + 2 y^{2} + 8 y = 20

x^{2} + 36 y^{2} - 24 x - 288 y + 611 = 0

169 x^{2} + 25 y^{2} = 4225

What is (4x)/(x^2+y^2)=-2 ?
The solution to (4x)/(x^2+y^2)=-2 is Ellipse with (h,k)=(-1,0),a=1,b=1