What is y^2-4y-4x^2+13=0 ?

The solution to y^2-4y-4x^2+13=0 is Hyperbola with (h,k)=(0,2),a= 3/2 ,b=3

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y^2-4y-4x^2+13=0

y^{2} - 4 y - 4 x^{2} + 13 = 0

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

Solution steps

y^{2} - 4 y - 4 x^{2} + 13 = 0

Rewrite

y^{2} - 4 y - 4 x^{2} + 13 = 0

in the form of a standard hyperbola equation

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

Therefore Hyperbola properties are:

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

16 y^{2} - x^{2} = 144

\frac{x ^{2}}{5} - \frac{y ^{2}}{9} = 1

\frac{x}{y} - \frac{y}{x} = \frac{1}{y}

(x - y) (x + y) = 2022

\frac{( y + 1 ) ^{2}}{9} - \frac{( x + 1 ) ^{2}}{16} = 1

What is y^2-4y-4x^2+13=0 ?
The solution to y^2-4y-4x^2+13=0 is Hyperbola with (h,k)=(0,2),a= 3/2 ,b=3