Geometry and TrigonometryVery hardRadius from an equation in general form
Geometry and Trigonometry practice question
The equation x² + y² − 10x + 4y + 13 = 0 represents a circle in the xy-plane. What is the radius of the circle?
- A. 4Correct
- B. 16
- C. √13
- D. 5
Answer: A. 4
Complete the square: (x − 5)² − 25 + (y + 2)² − 4 + 13 = 0, so (x − 5)² + (y + 2)² = 16. Radius = 4.
Why the other answers are wrong
- B. 16
- 16 is r², not r.
- C. √13
- √13 treats the constant 13 as r² without completing the square.
- D. 5
- 5 is the x-coordinate of the centre.
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