Example 1 · level 1
Find the radius of the circle x² + y² + 2x − 8y − 47 = 0.
Show solution
- g² + f² − c = 1 + 16 − (−47) = 64.
- Radius = √64 = 8.
Answer: 8
CLASS 11 MATHS · CONIC SECTIONS
Circle: centre and radius from the general equation
x² + y² + 2gx + 2fy + c = 0 has centre (−g, −f) and radius √(g² + f² − c). If x² and y² have a coefficient other than 1, divide through first.
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Worked examples
Example 2 · level 2
Find the centre of the circle x² + y² + 6x − 10y + 9 = 0.
- (3, −5)
- (6, −10)
- (−3, 5)
- (−6, 10)
Show solution
- g = 3, f = −5.
- Centre = (−g, −f) = (−3, 5).
Answer: (−3, 5)
Example 3 · level 3
Find the radius of the circle 4x² + 4y² + 16x − 24y + 36 = 0.
Show solution
- Divide by 4: x² + y² + 4x − 6y + 9 = 0.
- g² + f² − c = 4 + 9 − 9 = 4.
- Radius = √4 = 2.
Answer: 2