Geometry and TrigonometryHardEquation of a circle
Geometry and Trigonometry practice question
A circle is defined by the equation (x − 3)² + (y + 2)² = 25. What is the radius of the circle?
- A. 5Correct
- B. 25
- C. √5
- D. 12.5
Answer: A. 5
In (x − h)² + (y − k)² = r², the right side equals r², not r. Here r² = 25, so r = 5. Choice B (25) mistakes r² for the radius itself.
Why the other answers are wrong
- B. 25
- 25 is r², the value on the right side of the equation. Take the square root to get the radius: r = 5.
- C. √5
- √5 comes from taking the square root twice (√25 = 5, then √5). One square root of 25 is all you need: r = 5.
- D. 12.5
- 12.5 is 25 divided by 2, but the right side is r², not a diameter. Square-root 25 instead: r = 5.
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