# Homework Help: Circumferences and lines

1. May 5, 2010

### Taturana

1. The problem statement, all variables and given/known data

Find the angular coefficient of the line that is tangent to the following circumferences:
$$(x - 17)^{2} + y^{2} = 16$$
$$x^{2} + y^{2} = 16$$

2. Relevant equations

3. The attempt at a solution

I tried everything but nothing is working, please help me.

2. May 5, 2010

### Staff: Mentor

What did you try? Have you drawn a picture of the two circles (not circumferences)?

By "angular coefficient" do you mean slope?

3. May 5, 2010

### Taturana

Yeh I mean slope.

here is a picture:

[PLAIN]http://img94.imageshack.us/img94/2910/58393508.png [Broken]

I tried to make a system of equations such that: the distance between the center of the circumferences and the line is equal to 4 (that is the radius of the circumferences). But I end up to something like |17a + c| = |c| (considering the line as ax + by + c = 0), but it doesn't help me.

I tried to make two systems:
1: using the equation of the first circumference and the equation of the line
2: using the equation of the second circumference and the equation of the line
then I shared some variables between these systems (a and b, considering y = ax + b as the line). But the equations become very complicated and I think it's not the easiest way.

Someone can help me?

Last edited by a moderator: May 4, 2017
4. May 5, 2010

### Dick

Writing equations probably isn't the easiest way to solve it. Why don't you draw some right triangles in your picture?

5. May 5, 2010

### Taturana

Thank you, you helped me alot, now I solved.

6. May 6, 2010

### Staff: Mentor

I hope you realize that there is not just one tangent line that touches the circles. I count four of them.

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