What is x^2+1/3 y^2=x+y ?

The solution to x^2+1/3 y^2=x+y is Ellipse with (h,k)=(1/2 , 3/2),a=1,b=sqrt(3)

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x^2+1/3 y^2=x+y

x^{2} + \frac{1}{3} y^{2} = x + y

(h, k) = (\frac{1}{2}, \frac{3}{2}), a = 1, b = 3

Solution steps

x^{2} + \frac{1}{3} y^{2} = x + y

Rewrite

x^{2} + \frac{1}{3} y^{2} = x + y

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (\frac{1}{2}, \frac{3}{2}), a = 1, b = 3

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (\frac{1}{2}, \frac{3}{2}), b = 3, a = 1

What is x^2+1/3 y^2=x+y ?
The solution to x^2+1/3 y^2=x+y is Ellipse with (h,k)=(1/2 , 3/2),a=1,b=sqrt(3)