What is ((y+2)^2}{25}-\frac{(x-1)^2)/9 =1 ?

The solution to ((y+2)^2}{25}-\frac{(x-1)^2)/9 =1 is Hyperbola with (h,k)=(1,-2),a=5,b=3

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((y+2)^2}{25}-\frac{(x-1)^2)/9 =1

\frac{( y + 2 ) ^{2}}{25} - \frac{( x - 1 ) ^{2}}{9} = 1

(h, k) = (1, - 2), a = 5, b = 3

Solution steps

\frac{( y + 2 ) ^{2}}{25} - \frac{( x - 1 ) ^{2}}{9} = 1

Rewrite

\frac{( y + 2 ) ^{2}}{25} - \frac{( x - 1 ) ^{2}}{9} = 1

in the form of a standard hyperbola equation

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

Therefore Hyperbola properties are:

(h, k) = (1, - 2), a = 5, b = 3

4 x^{2} - 3 y^{2} - 12 = 0

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

x^{2} - y^{2} + 4 x - 2 y - 5 = 0

\frac{x ^{2}}{1} - \frac{y ^{2}}{15} = 1

x^{2} - 4 y^{2} + 6 x + 24 y - 31 = 0

What is ((y+2)^2}{25}-\frac{(x-1)^2)/9 =1 ?
The solution to ((y+2)^2}{25}-\frac{(x-1)^2)/9 =1 is Hyperbola with (h,k)=(1,-2),a=5,b=3