What is ((x-1)^2)/4-((y-3)^2)/9 =1 ?

The solution to ((x-1)^2)/4-((y-3)^2)/9 =1 is Hyperbola with (h,k)=(1,3),a=2,b=3

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((x-1)^2)/4-((y-3)^2)/9 =1

\frac{( x - 1 ) ^{2}}{4} - \frac{( y - 3 ) ^{2}}{9} = 1

(h, k) = (1, 3), a = 2, b = 3

Solution steps

\frac{( x - 1 ) ^{2}}{4} - \frac{( y - 3 ) ^{2}}{9} = 1

Rewrite

\frac{( x - 1 ) ^{2}}{4} - \frac{( y - 3 ) ^{2}}{9} = 1

in the form of a standard hyperbola equation

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

Therefore Hyperbola properties are:

(h, k) = (1, 3), a = 2, b = 3

x^{2} - 4 y^{2} - 4 \geq 0

9 x^{2} - 4 y^{2} - 72 x + 8 y + 176 = 0

\frac{( y - k ) ^{2}}{a ^{2}} - \frac{( x - h ) ^{2}}{b ^{2}} = 1

x, (x - 2)^{2} + (x - 3)^{2} = r (x)^{2}

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

What is ((x-1)^2)/4-((y-3)^2)/9 =1 ?
The solution to ((x-1)^2)/4-((y-3)^2)/9 =1 is Hyperbola with (h,k)=(1,3),a=2,b=3