What is 3x^2+6x=0.3y^2-6y ?

The solution to 3x^2+6x=0.3y^2-6y is Hyperbola with (h,k)=(-1,10),a=3sqrt(10),b=3

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3x^2+6x=0.3y^2-6y

3 x^{2} + 6 x = 0.3 y^{2} - 6 y

(h, k) = (- 1, 10), a = 310, b = 3

Solution steps

3 x^{2} + 6 x = 0.3 y^{2} - 6 y

Rewrite

3 x^{2} + 6 x = 0.3 y^{2} - 6 y

in the form of a standard hyperbola equation

\frac{( y - 10 ) ^{2}}{( 3 10 ) ^{2}} - \frac{( x - ( - 1 ) ) ^{2}}{3 ^{2}} = 1

Therefore Hyperbola properties are:

(h, k) = (- 1, 10), a = 310, b = 3

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

\frac{x ^{2}}{16} - \frac{y ^{2}}{81} = 1

x^{2} - 9 y^{2} + 8 x + 36 y - 29 = 0

7 y^{2} - 12 x^{2} = 84

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

What is 3x^2+6x=0.3y^2-6y ?
The solution to 3x^2+6x=0.3y^2-6y is Hyperbola with (h,k)=(-1,10),a=3sqrt(10),b=3