What is 16x^2-96x-25y^2+200y-656=0 ?

The solution to 16x^2-96x-25y^2+200y-656=0 is Hyperbola with (h,k)=(3,4),a=5,b=4

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16x^2-96x-25y^2+200y-656=0

16 x^{2} - 96 x - 25 y^{2} + 200 y - 656 = 0

(h, k) = (3, 4), a = 5, b = 4

Solution steps

16 x^{2} - 96 x - 25 y^{2} + 200 y - 656 = 0

Rewrite

16 x^{2} - 96 x - 25 y^{2} + 200 y - 656 = 0

in the form of a standard hyperbola equation

\frac{( x - 3 ) ^{2}}{5 ^{2}} - \frac{( y - 4 ) ^{2}}{4 ^{2}} = 1

Therefore Hyperbola properties are:

(h, k) = (3, 4), a = 5, b = 4

y^{2} = x^{2} + 17

y^{2} = x^{2} + 13

y^{2} = x^{2} + 14

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

\frac{( y - 13 ) ^{2}}{9} - \frac{( x - 10 ) ^{2}}{49} = 1

What is 16x^2-96x-25y^2+200y-656=0 ?
The solution to 16x^2-96x-25y^2+200y-656=0 is Hyperbola with (h,k)=(3,4),a=5,b=4