SOLUTION: Find the equation of the circle of radius 5 unts which lies within the circle x^2+y^2+14x+10y-26=0 and which touches the given circle at the point (-1,3).

Question 1051840: Find the equation of the circle of radius 5 unts which lies within the circle x^2+y^2+14x+10y-26=0 and which touches the given circle at the point (-1,3).
Found 2 solutions by josgarithmetic, ikleyn:
Answer by josgarithmetic(39629)   (Show Source): You can put this solution on YOUR website!
Make a plan for how to find the circle asked for.

Your circle to find has radius of 5, but the center of this circle is not known.

(*) What is the standard form for the GIVEN circle?
(*) What is the center point for the GIVEN circle?
(*) What is equation for the LINE connecting that center and point (-1,3)?
(*) Find the coordinate of the point on that line, 5 units from point (-1,3); you would use the Distance Formula to do this, and you will need to choose between two different answers. Once finally done, you have the point for the center of the CIRCLE YOU ARE LOOKING FOR.

That's a good possible plan. Each of those parts has several algebra steps. If it makes sense as listed above, then good! Do it. I have not yet tried to solve; only thought of the plan.
Answer by ikleyn(52873)   (Show Source): You can put this solution on YOUR website!
.
Similar problem was solved in the lesson
    - A problem on a circle touching another circle internally
in this site.

Look in it. It will give you an idea on how to solve your problem.

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