Geometry and TrigonometryHardSum of the x-intercepts of a circle
Geometry and Trigonometry practice question
In the xy-plane, the circle (x − 1)² + (y − 1)² = 25 crosses the x-axis at two points. What is the sum of the x-coordinates of those two points?
Answer: 2
At y = 0, (x − 1)² = 24, so x = 1 + √24 or x = 1 − √24. The square roots cancel in the sum, leaving 2.
Common wrong answers
- If you answered 0
- 0 forgets that the centre is not at the origin.
- If you answered 1
- 1 is the x-coordinate of the centre.
- If you answered 24
- 24 is (x − 1)².
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