1

I am doing a question on coordinate geometry.

It asks to find the points of intersection of the two circles:

$\\(x+1)^2+(y-2)^2=10$

and

$\\(x-1)^2+(y-3)^2=5$

And then find the area of the triangle formed by the two points and the origin.

I am wondering how to do this - when I sketch it, it looks like the line segment joining the points of intersection is perpendicular to the line segment joining the centers, but I can't prove this, and don't know what to do with it anyway.

Any help please!

harpomiel
  • 643
  • the line containing the points of intersection (given in the answer) is indeed perpendicular to the line containing the centers – J. W. Tanner Feb 12 '20 at 18:06

1 Answers1

2

Hint:

By subtracting the equations you get the radical line of them: $$4x+2y = 10.$$ Now plug $y =5-2x$ in to one of them and solve a quadratic equation on $x$...

J. W. Tanner
  • 60,406
nonuser
  • 90,026
  • I thought to do this but it felt weird. If we are solving simultaneous equations (1) and (2), I thought that if you subtract them to create a third equation, you can't then plug it back into one of the old ones? Although I suppose we do this when we subtract two linear equations and then substitute the single variable back into one of them.... – harpomiel Feb 14 '20 at 09:27