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The radius of the two circles are 5 unit respectively. The contact point between two circles is (1,2).the external general tangent equation between the two circle is 4x+3y=10.plz help me to find out the equations of the two circles?? I have just find out the slope of the equation.I really expect ur help cause I am a beginner. In this question I have added the radius of the circles.strong text

Momin Haq
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  • Ignore the equations and coordinates. You have two congruent circles, the point at which they touch, and a common external tangent. Draw a picture of that. Can you see how to get the radius of the circles from the picture? If so, then go back and see if you can calculate the radius from the equations and coordinates you are given. – Blue Sep 07 '18 at 18:24
  • Ah, I see that your previous question is identical to this one. Re-posting is not the way to call attention to your question. I'm voting to close. – Blue Sep 07 '18 at 18:29
  • I m sry if my question is not so acceptable. Plz accept my apology. But in the previous question I forgot to add some data like the radius of the circles. So its not actually duplicate but an edited version of the previous question. Plz forgive me if I did something against the terms and conditions. – Momin Haq Sep 07 '18 at 18:35
  • Don't feel bad. It's not a crime. :) Editing your previous question with the missing information was the correct course of action. Since the two questions are now identical, though, you should consider deleting this one. – Blue Sep 07 '18 at 18:38

1 Answers1

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The line between circle centers has a slope of $3/4$ (the negative reciprocal of the tangent equation) and also passes through point $(1, 2)$. The two circle centers are therefore located at $(1+4, 2+3)$ and $(1-4, 2-3)$ which are $(5, 5)$ and $(-3, -1)$

From the circle center locations and radius, you can determine the equations of the circles using $(x – h)^2 + (y – k)^2 = r^2$

enter image description here

Phil H
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