What is x^2-y^2-4x-6y=0 ?

The solution to x^2-y^2-4x-6y=0 is Hyperbola with (h,k)=(2,-3),a=sqrt(5),b=sqrt(5)

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x^2-y^2-4x-6y=0

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

(h, k) = (2, - 3), a = 5, b = 5

Solution steps

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

Rewrite

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

in the form of a standard hyperbola equation

\frac{( y - ( - 3 ) ) ^{2}}{( 5 ) ^{2}} - \frac{( x - 2 ) ^{2}}{( 5 ) ^{2}} = 1

Therefore Hyperbola properties are:

(h, k) = (2, - 3), a = 5, b = 5

(3 x - 3)^{2} - (2 y - 4)^{2} = 68

64 x^{2} - 100 y^{2} = 6400

\frac{x ^{2}}{49} - \frac{y ^{2}}{4} = 1

\frac{( y - 3 ) ^{2}}{16} - \frac{( x + 4 ) ^{2}}{25} = 1

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

What is x^2-y^2-4x-6y=0 ?
The solution to x^2-y^2-4x-6y=0 is Hyperbola with (h,k)=(2,-3),a=sqrt(5),b=sqrt(5)