Proving the Equation of a Circle (Black&White)
If you have a circle centered at point C(h, k) and radius r, its equation can be written as . Use the applet below to determine why.
PART A - Questions to think about:
1. What kind of a triangle is CDE? What special theorem you know about this type of triangle that connects all its sides into one formula?
2. Why are the lengths of two of the sides (x - h) and (y - k)? Slide point D along the circle. Do the lengths of the sides change?
Hint: check the Show Coordinates box!
PART B - Practice questions:
1. Write the equation of a circle with center at (3, 6) and radius 5.
2. Write the equation of a circle with center at (-3, 6) and radius 4.
3. Write the equation of a circle with center at the origin and radius 10.
Generalize: Write the equation of a circle with center at the origin and radius r.