What is ((x-4)^2)/9-((y+5)^2)/(16)=1 ?

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

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((x-4)^2)/9-((y+5)^2)/(16)=1

\frac{( x - 4 ) ^{2}}{9} - \frac{( y + 5 ) ^{2}}{16} = 1

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

Solution steps

\frac{( x - 4 ) ^{2}}{9} - \frac{( y + 5 ) ^{2}}{16} = 1

Rewrite

\frac{( x - 4 ) ^{2}}{9} - \frac{( y + 5 ) ^{2}}{16} = 1

in the form of a standard hyperbola equation

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

Therefore Hyperbola properties are:

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

(y - 4)^{2} - \frac{( x + 1 ) ^{2}}{16} = 1

144 y^{2} - 25 x^{2} = 3600

x^{2} - 25 y^{2} - 4 x + 75 y - 27 = 0

36 x^{2} - 4 y^{2} = 144

\frac{y ^{2}}{36} - \frac{x ^{2}}{49} = 1

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