What is 6x^2-3y^2+36x+30y=39 ?

The solution to 6x^2-3y^2+36x+30y=39 is Hyperbola with (h,k)=(-3,5),a=sqrt(3),b=sqrt(6)

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6x^2-3y^2+36x+30y=39

6 x^{2} - 3 y^{2} + 36 x + 30 y = 39

(h, k) = (- 3, 5), a = 3, b = 6

Solution steps

6 x^{2} - 3 y^{2} + 36 x + 30 y = 39

Rewrite

6 x^{2} - 3 y^{2} + 36 x + 30 y = 39

in the form of a standard hyperbola equation

\frac{( x - ( - 3 ) ) ^{2}}{( 3 ) ^{2}} - \frac{( y - 5 ) ^{2}}{( 6 ) ^{2}} = 1

Therefore Hyperbola properties are:

(h, k) = (- 3, 5), a = 3, b = 6

y^{2} - 4 = 9 x^{2}

(4 - 4 x)^{2} - 4 (2 k (x) + 2) (k (x) - 2) = 0

4 x^{2} - y^{2} - 32 x - 2 y = - 59

x^{2} - y^{2} = - 45

y^{2} = (x^{2} - 2 x)

What is 6x^2-3y^2+36x+30y=39 ?
The solution to 6x^2-3y^2+36x+30y=39 is Hyperbola with (h,k)=(-3,5),a=sqrt(3),b=sqrt(6)