What is 4x^2-16y^2-8x-96y-204=0 ?

The solution to 4x^2-16y^2-8x-96y-204=0 is Hyperbola with (h,k)=(1,-3),a=4,b=2

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4x^2-16y^2-8x-96y-204=0

4 x^{2} - 16 y^{2} - 8 x - 96 y - 204 = 0

(h, k) = (1, - 3), a = 4, b = 2

Solution steps

4 x^{2} - 16 y^{2} - 8 x - 96 y - 204 = 0

Rewrite

4 x^{2} - 16 y^{2} - 8 x - 96 y - 204 = 0

in the form of a standard hyperbola equation

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

Therefore Hyperbola properties are:

(h, k) = (1, - 3), a = 4, b = 2

f (x) f (x) = 4 x^{2} - x + 2

\frac{( x - 2 ) ^{2}}{4} - (\frac{( y - 2 )}{5})^{2} = 1

\frac{x ^{2}}{5} - \frac{y ^{2}}{7} = 1

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

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

What is 4x^2-16y^2-8x-96y-204=0 ?
The solution to 4x^2-16y^2-8x-96y-204=0 is Hyperbola with (h,k)=(1,-3),a=4,b=2