What is ((y-5)^2}{25}-\frac{(x+5)^2)/9 =1 ?

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

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((y-5)^2}{25}-\frac{(x+5)^2)/9 =1

\frac{( y - 5 ) ^{2}}{25} - \frac{( x + 5 ) ^{2}}{9} = 1

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

Solution steps

\frac{( y - 5 ) ^{2}}{25} - \frac{( x + 5 ) ^{2}}{9} = 1

Rewrite

\frac{( y - 5 ) ^{2}}{25} - \frac{( x + 5 ) ^{2}}{9} = 1

in the form of a standard hyperbola equation

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

Therefore Hyperbola properties are:

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

4 x^{2} - 9 y^{2} + 4 x + 36 y - 36 = 0

9 x^{2} - 16 y^{2} - 36 x + 96 y - 252 = 0

\frac{x ^{2} - 8 x + 16}{16} - \frac{y ^{2} + 4 y - 4}{9} = 0

50 x^{2} - 25 y^{2} + 144 x - 68 y - 75 = 0

4 x^{2} - y^{2} - 20 x - 10 y + 25 = 0

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