A circle question

[monokekie]

hey, could anyone please help me with a question?

it goes like this:

Find the coordinates of the points of intersection of the two curves:

4x^2+4y^2-60x-76y+536=0

and

x^2+y^2-10x-14y+49=0

Thank you sooo much....

[/0]

...[1]

...[2]

Multiply equation [2] by 4:

...[2']

Now subtract equation [2'] from equation [1]:



...[3]

Now sub [3] back into equation [2]:









From [2], When ,
But substituting and into the first equation, we see that it does not work; it is an extraneous solution.
You can visualise why doesn't work if you draw a graph of the two circles. For the each of , you will get two solutions, one of which will be at the intersection point, the other at a point horizontally opposite it. Thus I cannot emphasise more strongly that you check all of your solutions at the end of the problem.

From [2], When ,

Coordinates are

[monokekie]

Thanks sooo much