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 - 4 ) ^{2}}{4} + (y + 1)^{2} = 1

\frac{( ( x - 2 ) ^{2} )}{4} + \frac{( ( y + 4 ) ^{2} )}{16} = 1

36 X^{2} + 25 Y^{2} = 900

\frac{( x - 0 ) ^{2}}{2 ^{2}} + \frac{( y - ( - 3 ) ) ^{2}}{4 ^{2}} = 1

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

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