What is ((y+2)^2)/9-((x+4)^2)/(40)=1 ?

The solution to ((y+2)^2)/9-((x+4)^2)/(40)=1 is Hyperbola with (h,k)=(-4,-2),a=3,b=2sqrt(10)

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((y+2)^2)/9-((x+4)^2)/(40)=1

\frac{( y + 2 ) ^{2}}{9} - \frac{( x + 4 ) ^{2}}{40} = 1

(h, k) = (- 4, - 2), a = 3, b = 210

Solution steps

\frac{( y + 2 ) ^{2}}{9} - \frac{( x + 4 ) ^{2}}{40} = 1

Rewrite

\frac{( y + 2 ) ^{2}}{9} - \frac{( x + 4 ) ^{2}}{40} = 1

in the form of a standard hyperbola equation

\frac{( y - ( - 2 ) ) ^{2}}{3 ^{2}} - \frac{( x - ( - 4 ) ) ^{2}}{( 2 10 ) ^{2}} = 1

Therefore Hyperbola properties are:

(h, k) = (- 4, - 2), a = 3, b = 210

4 x^{2} - 9 y^{2} + 24 x + 18 y - 9 = 0

2 x^{2} - 3 y^{2} < 1

x^{2} = \frac{x}{2} + y^{2}

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

\frac{( x - 0 ) ^{2}}{3 ^{2}} - \frac{( y - 0 ) ^{2}}{4 ^{2}} = 1

What is ((y+2)^2)/9-((x+4)^2)/(40)=1 ?
The solution to ((y+2)^2)/9-((x+4)^2)/(40)=1 is Hyperbola with (h,k)=(-4,-2),a=3,b=2sqrt(10)