Question

Find the point of intersection of the lines given by x² + 3xy + 2y² + x – y – 6 = 0

Answer 1

 x² + 3xy + 2y² + x – y – 6 = 0

Comparing the given equation with

ax² + 2hxy + by² + 2gx + 2fy + c = 0, we get

a = 1, b = 2, h = `3/2`, g = `1/2`, f = `-1/2`, c = –6

Point of intersection = `((hf - bg)/(ab - h^2),(gh - af)/(ab - h^2))`

= `((3/2 xx -1/2 - 2 xx 1/2)/(1 xx 2 - 9/4), (1/2 xx 3/2 - 1 xx -1/2)/(1 xx 2 - 9/4))`

= `((-3/4 - 1)/(-1/4), (3/4 + 1/2)/(-1/4))`

= `((-7)/-1 , 5/-1)`

= (7, – 5)