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

The solution to ((y+9)^2}{49}-\frac{(x-1)^2)/9 =1 is Hyperbola with (h,k)=(1,-9),a=7,b=3

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

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

(h, k) = (1, - 9), a = 7, b = 3

Solution steps

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

Rewrite

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

in the form of a standard hyperbola equation

\frac{( y - ( - 9 ) ) ^{2}}{7 ^{2}} - \frac{( x - 1 ) ^{2}}{3 ^{2}} = 1

Therefore Hyperbola properties are:

(h, k) = (1, - 9), a = 7, b = 3

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

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

4 x^{2} + 8 x - y^{2} + 2 y = - 5

\frac{( y + 5 ) ^{2}}{25} - \frac{( x - 6 ) ^{2}}{16} = 1

2 x^{2} - 3 y^{2} = 15

What is ((y+9)^2}{49}-\frac{(x-1)^2)/9 =1 ?
The solution to ((y+9)^2}{49}-\frac{(x-1)^2)/9 =1 is Hyperbola with (h,k)=(1,-9),a=7,b=3