ACT Preparation / Unit 14 ACT 1316 worked example, 60 to 90 seconds
Finding a Circle's Center and Radius
The idea
When a circle's equation is expanded, its center and radius are found in four steps. First, group the x terms and the y terms, and move the constant to the right. Second, complete the square for x: add the square of half the x-coefficient to both sides. Third, do the same for y. Fourth, write both squares and read the center and the radius, the square root of the right side.
In practice
Worked example: x² + y² − 6x + 4y − 12 = 0. Step one: (x² − 6x) + (y² + 4y) = 12. Step two: adding 9 makes (x − 3)². Step three: adding 4 makes (y + 2)². The right side gains 13: (x − 3)² + (y + 2)² = 25. The center is (3, −2) and the radius is 5.
Where people slip
Add each completing number to the right side too; forgetting gives r² = 12 instead of 25.
Your place on the trail
Every lesson rests on earlier ones and opens later ones. Tap any to jump.
Something wrong in this lesson? Flag it · Sources for ACT Preparation