The equation of a circle, step by step
(x − h)² + (y − k)² = r² hides two things a student has to un-hide.
The question
Find the center and radius of x² + y² − 8x + 7 = 0.
Find the center and radius of x² + y² − 8x + 7 = 0
x² + y² − 8x + 7 = 0
(x² − 8x) + y² = −7
(x² − 8x + 16) + y² = 9
(x − 4)² + y² = 9
center (4, 0)r = 3
- Group the x terms and the y terms, and move the number to the other side.
- Complete the square: halve the x coefficient and square it (4² = 16). Add 16 to each side, so the right-hand side becomes −7 + 16 = 9.
- Each bracket is now a perfect square, and the right-hand side is r².
- So the center is (4, 0) and the radius is √9 = 3.
How it works.
- 01
Group the x terms and the y terms, and move the number to the other side.
- 02
Complete the square: halve the x coefficient and square it (4² = 16). Add 16 to each side, so the right-hand side becomes −7 + 16 = 9.
- 03
Each bracket is now a perfect square, and the right-hand side is r².
- 04
So the center is (4, 0) and the radius is √9 = 3.