Intro to Calculus- Summer Review: Problem 2

Use this sketch to explore how the equation of a line tangent to a circle is related to the equation of the circle.

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1. Move the center. What happens to the equation as a result?

2. Can you figure out how to get the radius of the circle to be 3? 4? 5?

3. What will be the radius of the circle with equation (x-2)²+(y-1)²=25?

4. Adjust the sketch so that the center of the circle is at (-2, 1) and the radius is 3. What's the equation?

5. Adjust the sketch so that the equation of the circle is (x-2)²+(y+1)²=4. Where is the center of the circle? What is the radius of the circle?

6. Check the box "Tangent Line".

7. What's the angle between the tangent line and the radius drawn to the point of tangency?

8. Adjust the sketch so that the equation of the circle is x²+y²=25 and the line is tangent to the circle at (4, 3). What will be the equation of the tangent line? Why?

Jeff Holcomb, Created with GeoGebra