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

\frac{4 x}{x ^{2} + y ^{2}} = 1

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

144 y^{2} + 63 x^{2} = 9072

\frac{( X - 3 ) ^{2}}{169} + \frac{( Y - 2 ) ^{2}}{144} = 1

25 x^{2} + 350 x + 16 y^{2} + 96 y - 2231 = 0

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