What is 16y^2-9x^2+54+64y-161=0 ?

The solution to 16y^2-9x^2+54+64y-161=0 is Hyperbola with (h,k)=(0,-2),a=(3sqrt(19))/4 ,b=sqrt(19)

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16y^2-9x^2+54+64y-161=0

16 y^{2} - 9 x^{2} + 54 + 64 y - 161 = 0

(h, k) = (0, - 2), a = \frac{3 19}{4}, b = 19

Solution steps

16 y^{2} - 9 x^{2} + 54 + 64 y - 161 = 0

Rewrite

16 y^{2} - 9 x^{2} + 54 + 64 y - 161 = 0

in the form of a standard hyperbola equation

\frac{( y - ( - 2 ) ) ^{2}}{( \frac{3 19}{4} ) ^{2}} - \frac{( x - 0 ) ^{2}}{( 19 ) ^{2}} = 1

Therefore Hyperbola properties are:

(h, k) = (0, - 2), a = \frac{3 19}{4}, b = 19

9 x^{2} - 4 y^{2} - 36 x + 16 y = 0

y^{2} - 36 x^{2} = 36

12 x^{2} + 6 y^{2} + 3 = 10 x^{2} + 10 y^{2} + 4

4 (- y)^{2} - (- x)^{2} = 36

4 x^{2} - 12 y^{2} + 8 x + 2 y = 2

What is 16y^2-9x^2+54+64y-161=0 ?
The solution to 16y^2-9x^2+54+64y-161=0 is Hyperbola with (h,k)=(0,-2),a=(3sqrt(19))/4 ,b=sqrt(19)