What is x^2-y^2-y+9=0 ?

The solution to x^2-y^2-y+9=0 is Hyperbola with (h,k)=(0,-1/2),a=(sqrt(37))/2 ,b=(sqrt(37))/2

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x^2-y^2-y+9=0

x^{2} - y^{2} - y + 9 = 0

(h, k) = (0, - \frac{1}{2}), a = \frac{37}{2}, b = \frac{37}{2}

Solution steps

x^{2} - y^{2} - y + 9 = 0

Rewrite

x^{2} - y^{2} - y + 9 = 0

in the form of a standard hyperbola equation

\frac{( y - ( - \frac{1}{2} ) ) ^{2}}{( \frac{37}{2} ) ^{2}} - \frac{( x - 0 ) ^{2}}{( \frac{37}{2} ) ^{2}} = 1

Therefore Hyperbola properties are:

(h, k) = (0, - \frac{1}{2}), a = \frac{37}{2}, b = \frac{37}{2}

16 x^{2} - 9 y^{2} - 96 x + 36 y - 36 = 0

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

\frac{( x + 1 ) ^{2}}{4} - \frac{( y + 1 ) ^{2}}{4} = 1

\frac{x ^{2}}{1 8 ^{2}} - \frac{y ^{2}}{3 5 ^{2}} = 1

x^{2} - 4 y^{2} - 2 x - 8 y + 1 = 0

What is x^2-y^2-y+9=0 ?
The solution to x^2-y^2-y+9=0 is Hyperbola with (h,k)=(0,-1/2),a=(sqrt(37))/2 ,b=(sqrt(37))/2