What is 4x^2-y^2-12y+36=0 ?

The solution to 4x^2-y^2-12y+36=0 is Hyperbola with (h,k)=(0,-6),a=6sqrt(2),b=3sqrt(2)

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4x^2-y^2-12y+36=0

4 x^{2} - y^{2} - 12 y + 36 = 0

(h, k) = (0, - 6), a = 62, b = 32

Solution steps

4 x^{2} - y^{2} - 12 y + 36 = 0

Rewrite

4 x^{2} - y^{2} - 12 y + 36 = 0

in the form of a standard hyperbola equation

\frac{( y - ( - 6 ) ) ^{2}}{( 6 2 ) ^{2}} - \frac{( x - 0 ) ^{2}}{( 3 2 ) ^{2}} = 1

Therefore Hyperbola properties are:

(h, k) = (0, - 6), a = 62, b = 32

9 x^{2} - 72 x - 4 y^{2} - 40 y + 44 = 36

4 x^{2} + 24 x - 2 y^{2} + 36 = 36

\frac{( y - 3 ) ^{2}}{4} - \frac{( x + 1 ) ^{2}}{16} = 1

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

x^{2} + 6 = y^{2} + 6 x - 2 y

What is 4x^2-y^2-12y+36=0 ?
The solution to 4x^2-y^2-12y+36=0 is Hyperbola with (h,k)=(0,-6),a=6sqrt(2),b=3sqrt(2)