G.6.6.2 Complete the Process
- Katie Akesson
Here is the equation of a circle: x² + y² - 6x - 20y + 105 = 0 Elena wants to find the center and radius of the circle. Here is what she’s done so far. Step 1: x² - 6x + y² - 20y = -105 Step 2: x² - 6x + 9 + y² - 20y +100 = -105 + 9 + 100 Step 3: x² - 6x + 9 + y² - 20y +100 = 4 1. What did Elena do in the first step? 2. Why did Elena add 9 and 100 to the left side of the equation in Step 2? 3. Why did Elena add 9 and 100 to the right side of the equation in Step 2? 4. What should Elena do next? 5. What are the center and radius of this circle? 6. Draw a graph of the circle below.
The goal was to rewrite the equation in the form (x - h)² + (y - k)² = r². Why did Elena want to do this?