What is 12x^2+6y^2+3=10x^2+10y^2+4 ?

The solution to 12x^2+6y^2+3=10x^2+10y^2+4 is Hyperbola with (h,k)=(0,0),a=sqrt(1/2),b= 1/2

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12x^2+6y^2+3=10x^2+10y^2+4

12 x^{2} + 6 y^{2} + 3 = 10 x^{2} + 10 y^{2} + 4

(h, k) = (0, 0), a = \frac{1}{2}, b = \frac{1}{2}

Solution steps

12 x^{2} + 6 y^{2} + 3 = 10 x^{2} + 10 y^{2} + 4

Rewrite

12 x^{2} + 6 y^{2} + 3 - 10 x^{2} - 10 y^{2} - 4 = 0

in the form of a standard hyperbola equation

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

Therefore Hyperbola properties are:

(h, k) = (0, 0), a = \frac{1}{2}, b = \frac{1}{2}

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

4 x^{2} - 12 y^{2} + 8 x + 2 y = 2

- 25 x^{2} + 4 y^{2} - 100 = 0

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

(x - 4)^{2} - 3 y^{2} + 6 y = 0

What is 12x^2+6y^2+3=10x^2+10y^2+4 ?
The solution to 12x^2+6y^2+3=10x^2+10y^2+4 is Hyperbola with (h,k)=(0,0),a=sqrt(1/2),b= 1/2