Module 3: Lines and Circles

We begin by creating a point P, which is attached to a slider a.

Question 1:

Notice that point P is defined at (2;a). What does the 2 represent in the point P? What does the a represent?

Now, we create a circle using C=Circle[P,2].

What can we say about this circle?

We will now create a line segment F=segment((4,0),(-4,0)) to intersect our circle.

In how many places does the line segment intersect the circle?

We can create points where the line and the circle intersect.

As the center of the circle changes (by sliding a), what do you notice about the intersection points?

Make a conjecture about how you know which intersection point is moving and which remains at the origin.

Now, let's test your conjecture by creating a different line segment and its intersection points with the circle.