What is ((y+7)^2)/9-((x-5)^2)/(16)=1 ?

The solution to ((y+7)^2)/9-((x-5)^2)/(16)=1 is Hyperbola with (h,k)=(5,-7),a=3,b=4

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((y+7)^2)/9-((x-5)^2)/(16)=1

\frac{( y + 7 ) ^{2}}{9} - \frac{( x - 5 ) ^{2}}{16} = 1

(h, k) = (5, - 7), a = 3, b = 4

Solution steps

\frac{( y + 7 ) ^{2}}{9} - \frac{( x - 5 ) ^{2}}{16} = 1

Rewrite

\frac{( y + 7 ) ^{2}}{9} - \frac{( x - 5 ) ^{2}}{16} = 1

in the form of a standard hyperbola equation

\frac{( y - ( - 7 ) ) ^{2}}{3 ^{2}} - \frac{( x - 5 ) ^{2}}{4 ^{2}} = 1

Therefore Hyperbola properties are:

(h, k) = (5, - 7), a = 3, b = 4

\frac{x ^{2}}{16} - \frac{y ^{2}}{12} = 1

3 x^{2} - 2 y^{2} - 12 x + 12 y + 29 = 0

9 x^{2} - 4 y^{2} + 36 x + 8 y + 33 = 0

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

144 x^{2} - 25 y^{2} + 864 x - 100 y - 2404 = 0

What is ((y+7)^2)/9-((x-5)^2)/(16)=1 ?
The solution to ((y+7)^2)/9-((x-5)^2)/(16)=1 is Hyperbola with (h,k)=(5,-7),a=3,b=4