What is 4x^2-24x-y^2-2y=-31 ?

The solution to 4x^2-24x-y^2-2y=-31 is Hyperbola with (h,k)=(3,-1),a=1,b=2

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4x^2-24x-y^2-2y=-31

4 x^{2} - 24 x - y^{2} - 2 y = - 31

(h, k) = (3, - 1), a = 1, b = 2

Solution steps

4 x^{2} - 24 x - y^{2} - 2 y = - 31

Rewrite

4 x^{2} - 24 x - y^{2} - 2 y = - 31

in the form of a standard hyperbola equation

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

Therefore Hyperbola properties are:

(h, k) = (3, - 1), a = 1, b = 2

9 y^{2} - 4 x^{2} + 32 x - 36 y - 64 = 0

x^{2} + (2 - y^{2}) = 9

4 x^{2} - y^{2} - 16 x + 2 y + 11 = 0

(\frac{( y + 4 )}{9})^{2} - (\frac{( x - 3 )}{25})^{2} = 1

\frac{( x - 3 ) ^{2}}{25} - \frac{( y - 1 ) ^{2}}{4} = 1

What is 4x^2-24x-y^2-2y=-31 ?
The solution to 4x^2-24x-y^2-2y=-31 is Hyperbola with (h,k)=(3,-1),a=1,b=2