help needed with conic section and hyperbolas

**bemidjibasser** · April 30th 2010, 11:33 AM

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!

**veljko** · April 30th 2010, 12:35 PM

$x^2 -4y^2 -2x-8y-7=0$ ;
$x^2 -2x +1 - 1 - (4x^2 + 8x +4) +4 -7 = 0$ ;
$(x-1)^2- (2y+2)^2 =4$ ;
$\frac{(x-1)^2}{4} - 4\cdot \frac{(y+1)^2}{4}=1$ ;

$\frac{(x-1)^2}{4} - \frac{(y+1)^2}{1}=1$ ( standard equation of the hyperbola is $\frac{(x-x_0)^2}{a^2} - \frac{(y-y_0)^2}{b^2}=1$ , center is $(x_0, y_0)$ )

Center for our hiperbola is: $(1, -1)$ .

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