Answer to Question #124658 in Geometry for desmond

Question

(b) Find the asymptotes of the hyperbola
x
2 − y
2 + 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

now we got the value of thye centre of this hyperbola (h,k) = (-1 , 1/2)

now , the equation of the two asymptote of this hyperbola are

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

y = 1/2 +1 +x

y = x + 3/2

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

y = 1/2 -x -1

y = -x - 1/2