What is 4x^2+24x-2y^2+36=36 ?

The solution to 4x^2+24x-2y^2+36=36 is Hyperbola with (h,k)=(-3,0),a=3,b=3sqrt(2)

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

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

(h, k) = (- 3, 0), a = 3, b = 32

Solution steps

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

Rewrite

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

in the form of a standard hyperbola equation

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

Therefore Hyperbola properties are:

(h, k) = (- 3, 0), a = 3, b = 32

\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

4 x^{2} - 24 x - y^{2} - 2 y = - 31

9 y^{2} - 4 x^{2} + 32 x - 36 y - 64 = 0

What is 4x^2+24x-2y^2+36=36 ?
The solution to 4x^2+24x-2y^2+36=36 is Hyperbola with (h,k)=(-3,0),a=3,b=3sqrt(2)