What is y^2-4x^2-12y-16x*16=0 ?

The solution to y^2-4x^2-12y-16x*16=0 is Hyperbola with (h,k)=(-32,6),a=sqrt(1015),b=2sqrt(1015)

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y^2-4x^2-12y-16x*16=0

y^{2} - 4 x^{2} - 12 y - 16 x \cdot 16 = 0

(h, k) = (- 32, 6), a = 1015, b = 21015

Solution steps

y^{2} - 4 x^{2} - 12 y - 16 x \cdot 16 = 0

Rewrite

y^{2} - 4 x^{2} - 12 y - 16 x \cdot 16 = 0

in the form of a standard hyperbola equation

\frac{( x - ( - 32 ) ) ^{2}}{( 1015 ) ^{2}} - \frac{( y - 6 ) ^{2}}{( 2 1015 ) ^{2}} = 1

Therefore Hyperbola properties are:

(h, k) = (- 32, 6), a = 1015, b = 21015

\frac{y ^{2}}{6} - 4 x^{2} = 1

y^{2} + 17 = 3 x^{2}

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

- x^{2} + y^{2} - 9 = 0

\frac{y ^{2}}{27} - \frac{x ^{2}}{9} = 1

What is y^2-4x^2-12y-16x*16=0 ?
The solution to y^2-4x^2-12y-16x*16=0 is Hyperbola with (h,k)=(-32,6),a=sqrt(1015),b=2sqrt(1015)