Advanced MathHardLength of a vertical chord of a circle
Advanced Math practice question
In the xy-plane, the vertical line x = 2 crosses the circle x² + y² = 40 at two points. What is the distance between those two points?
Answer: 12
At x = 2, y² = 36, so the points are (2, 6) and (2, −6) — a distance of 12 apart.
Common wrong answers
- If you answered 6
- 6 is the half-chord from the x-axis up; the full chord spans from −6 to 6.
- If you answered 36
- 36 is y²; the chord length is 6 − (−6) = 12.
- If you answered 40
- 40 is the radius squared; at x = 2 the remaining y² is 36, so the chord runs from −6 to 6.
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