What is 6(x+1/3)^2-6(y-1/2)^2+24=0 ?

The solution to 6(x+1/3)^2-6(y-1/2)^2+24=0 is Hyperbola with (h,k)=(-1/3 , 1/2),a=2,b=2

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6(x+1/3)^2-6(y-1/2)^2+24=0

6 (x + \frac{1}{3})^{2} - 6 (y - \frac{1}{2})^{2} + 24 = 0

(h, k) = (- \frac{1}{3}, \frac{1}{2}), a = 2, b = 2

Solution steps

6 (x + \frac{1}{3})^{2} - 6 (y - \frac{1}{2})^{2} + 24 = 0

Rewrite

6 (x + \frac{1}{3})^{2} - 6 (y - \frac{1}{2})^{2} + 24 = 0

in the form of a standard hyperbola equation

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

Therefore Hyperbola properties are:

(h, k) = (- \frac{1}{3}, \frac{1}{2}), a = 2, b = 2

(y)^{2} + (5)^{2} = (6 + 2 + x)^{2}

y^{2} - 9 x^{2} - 6 y - 18 x - 9 = 0

\frac{11 x ^{2}}{2} - 22 y^{2} + 11 x + 88 y - \frac{209}{2} = 0

- x^{2} + y^{2} - 4 x - 13 = 0

z^{2} + 1 0^{2} = 2 + q^{2} + \frac{9 6 ^{2}}{2}

What is 6(x+1/3)^2-6(y-1/2)^2+24=0 ?
The solution to 6(x+1/3)^2-6(y-1/2)^2+24=0 is Hyperbola with (h,k)=(-1/3 , 1/2),a=2,b=2