What is 2x^2-4y^2+8x-12y+64=0 ?

The solution to 2x^2-4y^2+8x-12y+64=0 is Hyperbola with (h,k)=(-2,-3/2),a=(sqrt(65))/2 ,b=sqrt(65/2)

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2x^2-4y^2+8x-12y+64=0

2 x^{2} - 4 y^{2} + 8 x - 12 y + 64 = 0

(h, k) = (- 2, - \frac{3}{2}), a = \frac{65}{2}, b = \frac{65}{2}

Solution steps

2 x^{2} - 4 y^{2} + 8 x - 12 y + 64 = 0

Rewrite

2 x^{2} - 4 y^{2} + 8 x - 12 y + 64 = 0

in the form of a standard hyperbola equation

\frac{( y - ( - \frac{3}{2} ) ) ^{2}}{( \frac{65}{2} ) ^{2}} - \frac{( x - ( - 2 ) ) ^{2}}{( \frac{65}{2} ) ^{2}} = 1

Therefore Hyperbola properties are:

(h, k) = (- 2, - \frac{3}{2}), a = \frac{65}{2}, b = \frac{65}{2}

4 x^{2} - y^{2} - 2 y - 5 = 0

4 x^{2} - 9 y^{2} - 24 x - 36 y - 36 = 0

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

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

x^{2} - y^{2} + 6 x - 4 y - 4 = 0

What is 2x^2-4y^2+8x-12y+64=0 ?
The solution to 2x^2-4y^2+8x-12y+64=0 is Hyperbola with (h,k)=(-2,-3/2),a=(sqrt(65))/2 ,b=sqrt(65/2)