SOLUTION: Find the equations of the two circles with centres on the x -axis and radius 4 which both touch the circle x^2 + y^2 - 2x - 6y + 9 =0 externally. Please help me sir

Algebra ->  Length-and-distance -> SOLUTION: Find the equations of the two circles with centres on the x -axis and radius 4 which both touch the circle x^2 + y^2 - 2x - 6y + 9 =0 externally. Please help me sir      Log On


   

Question 990646: Find the equations of the two circles with centres on the x -axis and radius 4 which both touch the circle x^2 + y^2 - 2x - 6y + 9 =0 externally. Please help me sir
Answer by ikleyn(52778) About Me  (Show Source):
You can put this solution on YOUR website!
.
x%5E2+%2B+y%5E2+-+2x+-+6y+%2B+9 = %28x-1%29%5E2+-+1+%2B+%28y-3%29%5E2.

So, your equation is

%28x-1%29%5E2+%2B+%28y-3%29%5E2 = 1.

It is the equation of the circle of the radius 1 with the center at the point (x,y) = (1,3).

Is it clear to you?

Next. The centers of the two new circles should be at he distance of 1 + 4 = 5 units from this point.

Is it clear?

So, you need to find the centers of these two circles in x-axis, that are at the distance of 5 units from the point (1,3).

Now make a sketch and complete the solution of the problem yourself.

Good luck.