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

The solution to y^2-3y-2=x^2 is Hyperbola with (h,k)=(0, 3/2),a=(sqrt(17))/2 ,b=(sqrt(17))/2

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y^2-3y-2=x^2

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

(h, k) = (0, \frac{3}{2}), a = \frac{17}{2}, b = \frac{17}{2}

Solution steps

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

Rewrite

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

in the form of a standard hyperbola equation

\frac{( y - \frac{3}{2} ) ^{2}}{( \frac{17}{2} ) ^{2}} - \frac{( x - 0 ) ^{2}}{( \frac{17}{2} ) ^{2}} = 1

Therefore Hyperbola properties are:

(h, k) = (0, \frac{3}{2}), a = \frac{17}{2}, b = \frac{17}{2}

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

\frac{y ^{2}}{4} - \frac{x ^{2}}{25} = 1

x^{2} - y^{2} = - \frac{3}{8}

9 x^{2} - 4 y^{2} - 36 x - 24 y = 36

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

What is y^2-3y-2=x^2 ?
The solution to y^2-3y-2=x^2 is Hyperbola with (h,k)=(0, 3/2),a=(sqrt(17))/2 ,b=(sqrt(17))/2