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### Finding the Equations of Two Circles

```
Date: 9/30/95 at 0:2:3
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:

(X^2)+(Y^2)+4X-2Y+1=0.

Please explain in detail.

Thanking you in advance,
PAKISTAN.
```

```
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
describes.

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
out.

-Doctor Andrew,  The Geometry Forum

```
Associated Topics:
High School Equations, Graphs, Translations

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