What is ((x+1)^2)/3-((y-1)^2)/5 =1 ?

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

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((x+1)^2)/3-((y-1)^2)/5 =1

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

(h, k) = (- 1, 1), a = 3, b = 5

Solution steps

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

Rewrite

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

in the form of a standard hyperbola equation

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

Therefore Hyperbola properties are:

(h, k) = (- 1, 1), a = 3, b = 5

- 36 x^{2} + y^{2} = 36

16 x^{2} - 9 y^{2} + 96 x + 36 y + 252 = 0

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

4 x^{2} - 9 y^{2} - 16 x + 18 y - 11 = 0

4 x^{2} - 5 y^{2} + 30 y = 65

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