What is ((x-5)^2)/4-((y-3)^2)/4 =1 ?

The solution to ((x-5)^2)/4-((y-3)^2)/4 =1 is Hyperbola with (h,k)=(5,3),a=2,b=2

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((x-5)^2)/4-((y-3)^2)/4 =1

\frac{( x - 5 ) ^{2}}{4} - \frac{( y - 3 ) ^{2}}{4} = 1

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

Solution steps

\frac{( x - 5 ) ^{2}}{4} - \frac{( y - 3 ) ^{2}}{4} = 1

Rewrite

\frac{( x - 5 ) ^{2}}{4} - \frac{( y - 3 ) ^{2}}{4} = 1

in the form of a standard hyperbola equation

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

Therefore Hyperbola properties are:

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

x^{2} - 4 y^{2} + 2 x - 16 y + 13 = 0

(x - 1)^{2} - (y - 10)^{2} = - 40

\frac{( y + 9 ) ^{2}}{49} - \frac{( x - 1 ) ^{2}}{9} = 1

y^{2} + 7 = x^{2} - 8

\frac{( a ^{2} + b ^{2} )}{2} - 2 (a^{2} - b^{2}) = - 15

What is ((x-5)^2)/4-((y-3)^2)/4 =1 ?
The solution to ((x-5)^2)/4-((y-3)^2)/4 =1 is Hyperbola with (h,k)=(5,3),a=2,b=2