What is (x-5)^2-3(y+2)^2=4 ?

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

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(x-5)^2-3(y+2)^2=4

(x - 5)^{2} - 3 (y + 2)^{2} = 4

(h, k) = (5, - 2), a = 2, b = \frac{2}{3}

Solution steps

(x - 5)^{2} - 3 (y + 2)^{2} = 4

Rewrite

(x - 5)^{2} - 3 (y + 2)^{2} = 4

in the form of a standard hyperbola equation

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

Therefore Hyperbola properties are:

(h, k) = (5, - 2), a = 2, b = \frac{2}{3}

\frac{y ^{2}}{8} - \frac{x ^{2}}{5} = 1

7 x^{2} - 24 y^{2} = 41

9 y^{2} - 4 x^{2} - 36 y - 8 x = 4

- x^{2} + y^{2} - 8 y - 9 = 0

\frac{2 x ^{2}}{25} - \frac{( y - 3 ) ^{2}}{49} = 1

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