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

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

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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 = \frac{3}{2}, b = \frac{1}{2}

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 a standard hyperbola equation

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

Therefore Hyperbola properties are:

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

x^{2} - y^{2} + 1 = 0

x, x^{2} - 48 x + 640 = m (x)^{2}

25 y^{2} - 300 y - x^{2} + 2 x + 799 = 0

\frac{x ^{2}}{36} - \frac{y ^{2}}{121} = 1

\frac{x ^{2} - y ^{2}}{11 x \cdot 2} = 4

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