What is y^2-16x^2-8y-96x-144=0 ?

The solution to y^2-16x^2-8y-96x-144=0 is Hyperbola with (h,k)=(-3,4),a=4,b=1

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y^2-16x^2-8y-96x-144=0

y^{2} - 16 x^{2} - 8 y - 96 x - 144 = 0

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

Solution steps

y^{2} - 16 x^{2} - 8 y - 96 x - 144 = 0

Rewrite

y^{2} - 16 x^{2} - 8 y - 96 x - 144 = 0

in the form of a standard hyperbola equation

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

Therefore Hyperbola properties are:

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

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

9 x^{2} - 4 y^{2} - 54 x - 40 y - 55 = 0

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

\frac{( y - 1 ) ^{2}}{9} - \frac{( x - 3 ) ^{2}}{16} = 1

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

What is y^2-16x^2-8y-96x-144=0 ?
The solution to y^2-16x^2-8y-96x-144=0 is Hyperbola with (h,k)=(-3,4),a=4,b=1