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

The solution to 3x^2+y^2=x+y is Ellipse with (h,k)=(1/6 , 1/2),a= 1/3 ,b=sqrt(1/3)

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3x^2+y^2=x+y

3 x^{2} + y^{2} = x + y

(h, k) = (\frac{1}{6}, \frac{1}{2}), a = \frac{1}{3}, b = \frac{1}{3}

Solution steps

3 x^{2} + y^{2} = x + y

Rewrite

3 x^{2} + y^{2} = x + y

in the form of the standard ellipse equation

\frac{( x - \frac{1}{6} ) ^{2}}{( \frac{1}{3} ) ^{2}} + \frac{( y - \frac{1}{2} ) ^{2}}{( \frac{1}{3} ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (\frac{1}{6}, \frac{1}{2}), a = \frac{1}{3}, b = \frac{1}{3}

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (\frac{1}{6}, \frac{1}{2}), b = \frac{1}{3}, a = \frac{1}{3}

9 x^{2} + 27 y^{2} - 6 x - 108 y + 82 = 0

\frac{x ^{2}}{2} + \frac{y ^{2}}{7} = 1

2 (x^{2} + 3 x + 2.25) + y (3 y - 1 + 1) = - 4 + 4.5 + 1

9 x^{2} + 26 y^{2} = 60

8 x^{2} + 9 y^{2} - 16 x - 54 y + 17 = 0

What is 3x^2+y^2=x+y ?
The solution to 3x^2+y^2=x+y is Ellipse with (h,k)=(1/6 , 1/2),a= 1/3 ,b=sqrt(1/3)