What is (4x)/(x^2+y^2)=1 ?

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

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(4x)/(x^2+y^2)=1

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

(h, k) = (2, 0), a = 2, b = 2

Solution steps

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

Rewrite

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

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (2, 0), a = 2, b = 2

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (2, 0), b = 2, a = 2

\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

\frac{( x - 3 ) ^{2}}{9} + \frac{( y + 4 ) ^{2}}{25} = 1

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