Points where tangent line touches 2 circles

  • Thread starter madgab89
  • Start date
  • #1
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Homework Statement


On the circles y^2+x^2=1 and y^2+(x-3)^2=4
There is a line with positive slope that is tangent to both circles. Determine the points at which this tangent touches each circle.

Homework Equations


the derivative of the first circle i found:
y'=-x/y

the derivative of the second cirlce I found:
y'=-2x+6/2y

and also
x^2+y^2=1


The Attempt at a Solution



so I have these equations for slopes:
-x1/y1

-2x2+6/2y2

y2-y1/x2-x1

Now where do I go from here, can someone get me started with the rearranging or whatever?
 

Answers and Replies

  • #2
rock.freak667
Homework Helper
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31
What I think you should do is put the tangent as y=mx+c, then solve this with y^2+x^2=1, and when you simplify it into the form ax^2+bx+c=0, b^2-4ac=0 since it is a tangent. Then do the same with y^2+(x-3)^2=4 and you will get two equations in m and c.
 
  • #3
Dick
Science Advisor
Homework Helper
26,263
619

Homework Statement


On the circles y^2+x^2=1 and y^2+(x-3)^2=4
There is a line with positive slope that is tangent to both circles. Determine the points at which this tangent touches each circle.

Homework Equations


the derivative of the first circle i found:
y'=-x/y

the derivative of the second cirlce I found:
y'=-2x+6/2y

and also
x^2+y^2=1


The Attempt at a Solution



so I have these equations for slopes:
-x1/y1

-2x2+6/2y2

y2-y1/x2-x1

Now where do I go from here, can someone get me started with the rearranging or whatever?

I think the main problem is that you haven't written down any equations yet. Those are expressions, not equations. Put in some equal signs. Do you want to say that all of those are equal to the unknown slope m?
 

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