What is 16x^2-64x-9y^2-54y+1=0 ?

The solution to 16x^2-64x-9y^2-54y+1=0 is Hyperbola with (h,k)=(2,-3),a=sqrt(2),b= 3/(2sqrt(2))

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16x^2-64x-9y^2-54y+1=0

16 x^{2} - 64 x - 9 y^{2} - 54 y + 1 = 0

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

Solution steps

16 x^{2} - 64 x - 9 y^{2} - 54 y + 1 = 0

Rewrite

16 x^{2} - 64 x - 9 y^{2} - 54 y + 1 = 0

in the form of a standard hyperbola equation

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

Therefore Hyperbola properties are:

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

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

7 x^{2} - 9 y^{2} - 63 = 0

9 y^{2} - 4 x^{2} - 8 x - 12 y + 16 = 0

\frac{( x + 2 ) ^{2}}{4} - \frac{( y - 1 ) ^{2}}{25} = 1

x^{2} - 2 y^{2} = 3

What is 16x^2-64x-9y^2-54y+1=0 ?
The solution to 16x^2-64x-9y^2-54y+1=0 is Hyperbola with (h,k)=(2,-3),a=sqrt(2),b= 3/(2sqrt(2))