What is (x-4)^2-3y^2+6y=0 ?

The solution to (x-4)^2-3y^2+6y=0 is Hyperbola with (h,k)=(4,1),a=1,b=sqrt(3)

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(x-4)^2-3y^2+6y=0

(x - 4)^{2} - 3 y^{2} + 6 y = 0

(h, k) = (4, 1), a = 1, b = 3

Solution steps

(x - 4)^{2} - 3 y^{2} + 6 y = 0

Rewrite

(x - 4)^{2} - 3 y^{2} + 6 y = 0

in the form of a standard hyperbola equation

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

Therefore Hyperbola properties are:

(h, k) = (4, 1), a = 1, b = 3

(16 x^{2}) - (9 y^{2}) - 32 x - 54 y + 79 = 0

2 x^{2} - 3 x - 2 y^{2} + 6 y = 1

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

y^{2} - z^{2} = 1

\frac{( y - h ) ^{2}}{49} - \frac{( x - k ) ^{2}}{81} = 1

What is (x-4)^2-3y^2+6y=0 ?
The solution to (x-4)^2-3y^2+6y=0 is Hyperbola with (h,k)=(4,1),a=1,b=sqrt(3)