Geometry: An Interactive Journey to Mastery

Lesson 20: The Equation of a Circle

 )LQGWKHHTXDWLRQRIWKHFLUFOHZLWKFHQWHUͼ௘í௘ͽWDQJHQWWRWKHy-axis.

 Consider the circles with the following equations.

22

xyxy  922 25. 12 100.

D௘ͽ :KDWDUHWKHUDGLLRIWKHFLUFOHV"

E௘ͽ :KDWLVWKHGLVWDQFHEHWZHHQWKHFHQWHUVRIWKHFLUFOHV"

F௘ͽ 0DNHDURXJKVNHWFKRIWKHWZRFLUFOHVWRH[SODLQZK\WKHFLUFOHVPXVWEHWDQJHQWWRRQHDQRWKHU

 Consider the circles with the following equations.

22

xyxy  322 2. 3 32.

D௘ͽ :KDWDUHWKHUDGLLRIWKHFLUFOHV"

E௘ͽ :KDWLVWKHGLVWDQFHEHWZHHQWKHFHQWHUVRIWKHFLUFOHV"

F௘ͽ 0DNHDURXJKVNHWFKRIWKHWZRFLUFOHVWRH[SODLQZK\WKHFLUFOHVPXVWEHWDQJHQWWRRQHDQRWKHU

 Let A ͼ௘௘ͽDQGB ͼ௘í௘ͽ:ULWHWKHHTXDWLRQRIWKHFLUFOHWKDWKDVAB as its diameter.