What is 3x^2-3y^2+30x-6y+25=0 ?

The solution to 3x^2-3y^2+30x-6y+25=0 is Hyperbola with (h,k)=(-5,-1),a=sqrt(47/3),b=sqrt(47/3)

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3x^2-3y^2+30x-6y+25=0

3 x^{2} - 3 y^{2} + 30 x - 6 y + 25 = 0

(h, k) = (- 5, - 1), a = \frac{47}{3}, b = \frac{47}{3}

Solution steps

3 x^{2} - 3 y^{2} + 30 x - 6 y + 25 = 0

Rewrite

3 x^{2} - 3 y^{2} + 30 x - 6 y + 25 = 0

in the form of a standard hyperbola equation

\frac{( x - ( - 5 ) ) ^{2}}{( \frac{47}{3} ) ^{2}} - \frac{( y - ( - 1 ) ) ^{2}}{( \frac{47}{3} ) ^{2}} = 1

Therefore Hyperbola properties are:

(h, k) = (- 5, - 1), a = \frac{47}{3}, b = \frac{47}{3}

\frac{( x - 7 ) ^{2}}{a ^{2}} - \frac{( y + 6 ) ^{2}}{b ^{2}} = 1

\frac{( y + 2 ) ^{2}}{9} - \frac{( x - 1 ) ^{2}}{4} = 1

\frac{( y + 2 ) ^{2}}{36} - x^{2} = 1

\frac{( y - 2 ) ^{2}}{4} - \frac{( x - 2 ) ^{2}}{9} = 1

16 x^{2} - 9 y^{2} = 576

What is 3x^2-3y^2+30x-6y+25=0 ?
The solution to 3x^2-3y^2+30x-6y+25=0 is Hyperbola with (h,k)=(-5,-1),a=sqrt(47/3),b=sqrt(47/3)