CIRCLES: I am having trouble getting the right answer: "Show that circles with equation x^2 + y^2 -2x -10y +6=0 and (x-7)^2 +(y-2)^2=5 touch each other and determine the coordinates of their point of contact".

Question

anonymous · Answer

first i got both equations in terms of x^2 and y^2

then i equated them 

then i solved for x - i should get a quadratic equation but it ended up having no solutions

ankit042 · Answer

find the centers and radius of both circles. Now calculate the distance between the centers

anonymous · Answer

(7,2) √5

(1,5) √20

is what i got.

ankit042 · Answer

Now if distance (d) is equal sum of radii of two circles then they touch each other externally. if difference of radii is equal to distance then they touch internally

ankit042 · Answer

Calculate the distance(d) between centers

anonymous · Answer

Yes i know that - what i need help with is finding the point of contact as in the point where they touch. Can you help me with this?

ankit042 · Answer

you can read it here http://math.stackexchange.com/questions/256100/how-can-i-find-the-points-at-which-two-circles-intersect

anonymous · Answer

mmmm - their methods were a bit confusing - does anyone have a method to see if they can get the answer? I know a method - but for some unknown reason, I am getting 'no solution'. The answer is (3,5) but I can't seem to get it.

directrix · Answer

@BarbaraKara  Is the answer (3,5) or (5,3)?

anonymous · Answer

Woops! The correct answer is (5,3)

directrix · Answer

The question is how to get that. I'm working on the algebra to see what happens - to see if I get the "no solution" answer you did.

anonymous · Answer

Thank you so much - Really appreciate it.

anonymous · Answer

I have to go now, but I look forward to seeing how you go.
Thanks again :)

directrix · Answer

Okay. I'm lost in a sea of symbols at the moment.