The Math Forum

Ask Dr. Math - Questions and Answers from our Archives
Associated Topics || Dr. Math Home || Search Dr. Math

Finding the Equations of Two Circles

Date: 9/30/95 at 0:2:3
From: Badar Khushnood
Subject: HELP !!!

Dr. Math,

I have a question.  Please solve this for me.

Find the equation of the circles with the center at (4,-7) and
touching (externally and internally) the circle with the equation:


Please explain in detail.

Thanking you in advance,

Date: 9/30/95 at 1:32:28
From: Doctor Andrew
Subject: Re: HELP !!!

We won't solve it for you, but we'll try give you a good start.  
The first step is to figure out what circle the given equation 

There is some circle with center at (a,b) and radius r that is 
described by that equation. The formula for a circle with center 
at (a,b) and radius r is:

(X-a)^2 + (Y-b)^2 = r^2

So see if you can rewrite the given equation in that format.  
Think about what an expression like (X-a)^2 expands to.  Once you 
know what circle this is, you might want to graph the known circle 
and the center of the unknown circle.  You'll then want to figure 
out which radii (plural of radius) will cause the circle at (4,-7) 
of that radius to touch the other circle. 

Good luck!  If you get stuck, tell us where and we'll help you 

-Doctor Andrew,  The Geometry Forum

Associated Topics:
High School Equations, Graphs, Translations

Search the Dr. Math Library:

Find items containing (put spaces between keywords):
Click only once for faster results:

[ Choose "whole words" when searching for a word like age.]

all keywords, in any order at least one, that exact phrase
parts of words whole words

Submit your own question to Dr. Math

[Privacy Policy] [Terms of Use]

Math Forum Home || Math Library || Quick Reference || Math Forum Search

Ask Dr. MathTM
© 1994- The Math Forum at NCTM. All rights reserved.