find the intersection of these

2x^2+2y^2-4x+9y+4=0

x^2+y^2+x+12y+8=0

its very hard.. it tried substitution and yielded complex numbers.. pls help

Printable View

- Nov 21st 2010, 02:43 AMaeroflixsolving a conic intersection
find the intersection of these

2x^2+2y^2-4x+9y+4=0

x^2+y^2+x+12y+8=0

its very hard.. it tried substitution and yielded complex numbers.. pls help - Nov 21st 2010, 03:59 AMHallsofIvy
Have you tried: multiply the second equation by 2 and subtract from the first equation. That leaves a linear equation in x and y. Solve that for, say, y as a linear function of x and substitute into either of the original equations. That gives you a quadratic equation for x.

Yes, such an equation might well have complex roots. If so, what would that tell you about the intersection of the two circles?