Answer to Question #124558 in Analytic Geometry for nana

Question

Find the asymptotes of the hyperbola x² −y² + 2x + y + 9 = 0.

Answer 1

x² - y² + 2x + y + 9 = 0

x² + 2x - y² + y = - 9

-(x² + 2x)/9 + (y² - y) /9 = 1

-{(x + 1)² - 1}/9 +{(y - 1/2)² - 1/4}/9 =

1 + 1/9 - 1/36

{(y - 1/2)²}/9 - {(x+1)²}/9 =1.

The above is the equation of a hyperbola whose transverseaxis is parallel to the y-axis. Thus, the center of the hyperbola is (-1,1/2). Thus, the equations of the two assymptotes of the hyperbola are:

(i) y=1/2 + x - (-1)

y= x + 3/2

(ii)y=1/2 - x + (-1)

y= -x - 1/2