What is (2x)/(x^2+y^2)<-1 ?

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

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(2x)/(x^2+y^2)<-1

\frac{2 x}{x ^{2} + y ^{2}} < - 1

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

Solution steps

\frac{2 x}{x ^{2} + y ^{2}} < - 1

Rewrite

\frac{2 x}{x ^{2} + y ^{2}} < - 1

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{1000}{1 + x ^{2} + y ^{2}} = 200

5 x^{2} + 10 y^{2} - 80 = 0

9 y^{2} + 16 x^{2} - 90 y - 96 x + 225 = 0

3 x^{2} + 2 y^{2} - 12 = 0

\frac{y ^{2}}{16} + \frac{x ^{2}}{25} = 1

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