Given the equation x^2-4y^2-2x-8y-7=0 how do you find the coordinates of the center of the hyperbola? Thanks for the help in advance!
$\displaystyle x^2 -4y^2 -2x-8y-7=0$;
$\displaystyle x^2 -2x +1 - 1 - (4x^2 + 8x +4) +4 -7 = 0$;
$\displaystyle (x-1)^2- (2y+2)^2 =4$;
$\displaystyle \frac{(x-1)^2}{4} - 4\cdot \frac{(y+1)^2}{4}=1$;
$\displaystyle \frac{(x-1)^2}{4} - \frac{(y+1)^2}{1}=1$ ( standard equation of the hyperbola is $\displaystyle \frac{(x-x_0)^2}{a^2} - \frac{(y-y_0)^2}{b^2}=1$, center is $\displaystyle (x_0, y_0)$)
Center for our hiperbola is: $\displaystyle (1, -1)$.