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

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

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

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

(h, k) = (- 2, - 3), a = 3, b = \frac{5}{2}

Solution steps

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

Rewrite

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

in the form of a standard hyperbola equation

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

Therefore Hyperbola properties are:

(h, k) = (- 2, - 3), a = 3, b = \frac{5}{2}

y^{2} - z^{2} = 16

y^{2} = x^{2} + 169

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

\frac{( y - 4 ) ^{2}}{28} - \frac{( x + 1 ) ^{2}}{21} = 1

\frac{( y + 9 ) ^{2}}{92} - \frac{( x + 8 ) ^{2}}{36} = 17

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