What is -3(x^2-2x+1)+(y^2+4y+2)-2=-11 ?

The solution to -3(x^2-2x+1)+(y^2+4y+2)-2=-11 is Hyperbola with (h,k)=(1,-2),a=sqrt(7/3),b=sqrt(7)

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-3(x^2-2x+1)+(y^2+4y+2)-2=-11

- 3 (x^{2} - 2 x + 1) + (y^{2} + 4 y + 2) - 2 = - 11

(h, k) = (1, - 2), a = \frac{7}{3}, b = 7

Solution steps

- 3 (x^{2} - 2 x + 1) + y^{2} + 4 y + 2 - 2 = - 11

Rewrite

- 3 (x^{2} - 2 x + 1) + y^{2} + 4 y + 2 - 2 = - 11

in the form of a standard hyperbola equation

\frac{( x - 1 ) ^{2}}{( \frac{7}{3} ) ^{2}} - \frac{( y - ( - 2 ) ) ^{2}}{( 7 ) ^{2}} = 1

Therefore Hyperbola properties are:

(h, k) = (1, - 2), a = \frac{7}{3}, b = 7

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

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

x^{2} - y^{2} - 2 x - 4 y - 7 = 0

\frac{( y - 4 ) ^{2}}{25} - \frac{( x + 1 ) ^{2}}{4} = 1

y \frac{1}{3} y - x^{2} + 2 x = - 5

What is -3(x^2-2x+1)+(y^2+4y+2)-2=-11 ?
The solution to -3(x^2-2x+1)+(y^2+4y+2)-2=-11 is Hyperbola with (h,k)=(1,-2),a=sqrt(7/3),b=sqrt(7)