What is x^2-y^2+3y=0 ?

The solution to x^2-y^2+3y=0 is Hyperbola with (h,k)=(0, 3/2),a= 3/2 ,b= 3/2

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x^2-y^2+3y=0

x^{2} - y^{2} + 3 y = 0

(h, k) = (0, \frac{3}{2}), a = \frac{3}{2}, b = \frac{3}{2}

Solution steps

x^{2} - y^{2} + 3 y = 0

Rewrite

x^{2} - y^{2} + 3 y = 0

in the form of a standard hyperbola equation

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

Therefore Hyperbola properties are:

(h, k) = (0, \frac{3}{2}), a = \frac{3}{2}, b = \frac{3}{2}

\frac{y ^{2}}{9} - \frac{x ^{2}}{7} = 1

4 x^{(2)} - 4 y^{(2)} - 4 x + 8 y - 19 = 0

- \frac{y ^{2}}{4} + \frac{z ^{2}}{9} = 1

10 x^{2} - 64 y^{2} - 140 x + 768 y - 2454 = 0

y^{2} - 16 x^{2} = 1

What is x^2-y^2+3y=0 ?
The solution to x^2-y^2+3y=0 is Hyperbola with (h,k)=(0, 3/2),a= 3/2 ,b= 3/2