What is 16y^2-32y-9x^2-18x=137 ?

The solution to 16y^2-32y-9x^2-18x=137 is Hyperbola with (h,k)=(-1,1),a=3,b=4

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16y^2-32y-9x^2-18x=137

16 y^{2} - 32 y - 9 x^{2} - 18 x = 137

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

Solution steps

16 y^{2} - 32 y - 9 x^{2} - 18 x = 137

Rewrite

16 y^{2} - 32 y - 9 x^{2} - 18 x = 137

in the form of a standard hyperbola equation

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

Therefore Hyperbola properties are:

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

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

25 x^{2} + 16 y^{2} = 400

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

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

x^{2} + y^{2} = 121

What is 16y^2-32y-9x^2-18x=137 ?
The solution to 16y^2-32y-9x^2-18x=137 is Hyperbola with (h,k)=(-1,1),a=3,b=4