What is x^2-y^2-4x-12y+15=0 ?

The solution to x^2-y^2-4x-12y+15=0 is Hyperbola with (h,k)=(2,-6),a=sqrt(47),b=sqrt(47)

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x^2-y^2-4x-12y+15=0

x^{2} - y^{2} - 4 x - 12 y + 15 = 0

(h, k) = (2, - 6), a = 47, b = 47

Solution steps

x^{2} - y^{2} - 4 x - 12 y + 15 = 0

Rewrite

x^{2} - y^{2} - 4 x - 12 y + 15 = 0

in the form of a standard hyperbola equation

\frac{( y - ( - 6 ) ) ^{2}}{( 47 ) ^{2}} - \frac{( x - 2 ) ^{2}}{( 47 ) ^{2}} = 1

Therefore Hyperbola properties are:

(h, k) = (2, - 6), a = 47, b = 47

3 x^{2} - 2 y^{2} = 12

\frac{- x ^{2}}{5} + \frac{y ^{2}}{7} = 1

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

(x - 2 y) (x + 2 y) = 4

16 x^{2} - 3 y^{2} - 32 x + 12 y - 44 = 0

What is x^2-y^2-4x-12y+15=0 ?
The solution to x^2-y^2-4x-12y+15=0 is Hyperbola with (h,k)=(2,-6),a=sqrt(47),b=sqrt(47)