What is 4x^2-9(y+1)^2=36 ?

The solution to 4x^2-9(y+1)^2=36 is Hyperbola with (h,k)=(0,-1),a=3,b=2

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4x^2-9(y+1)^2=36

4 x^{2} - 9 (y + 1)^{2} = 36

(h, k) = (0, - 1), a = 3, b = 2

Solution steps

4 x^{2} - 9 (y + 1)^{2} = 36

Rewrite

4 x^{2} - 9 (y + 1)^{2} = 36

in the form of a standard hyperbola equation

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

Therefore Hyperbola properties are:

(h, k) = (0, - 1), a = 3, b = 2

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

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

x^{2} - y^{2} = 8

4 x^{2} - 8 x - y^{2} - 2 y - 13 = 0

3 x^{2} - 2 y^{2} + 24 x + 12 y + 24 = 0

What is 4x^2-9(y+1)^2=36 ?
The solution to 4x^2-9(y+1)^2=36 is Hyperbola with (h,k)=(0,-1),a=3,b=2