What is ((y+4)^2)/9-((x-3)^2)/(25)=1 ?

The solution to ((y+4)^2)/9-((x-3)^2)/(25)=1 is Hyperbola with (h,k)=(3,-4),a=3,b=5

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((y+4)^2)/9-((x-3)^2)/(25)=1

\frac{( y + 4 ) ^{2}}{9} - \frac{( x - 3 ) ^{2}}{25} = 1

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

Solution steps

\frac{( y + 4 ) ^{2}}{9} - \frac{( x - 3 ) ^{2}}{25} = 1

Rewrite

\frac{( y + 4 ) ^{2}}{9} - \frac{( x - 3 ) ^{2}}{25} = 1

in the form of a standard hyperbola equation

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

Therefore Hyperbola properties are:

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

25 y^{2} - 16 x^{2} - 400 = 0

2 x^{2} - 2 y^{2} - 20 x + 16 y + 16 = 0

y^{2} - x^{2} + 1 = 50

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

a^{2} + 1 0^{2} + 1 1^{2} = c^{2}

What is ((y+4)^2)/9-((x-3)^2)/(25)=1 ?
The solution to ((y+4)^2)/9-((x-3)^2)/(25)=1 is Hyperbola with (h,k)=(3,-4),a=3,b=5