Advanced MathHardIntersection of a circle and a line through the origin
Advanced Math practice question
In the xy-plane, the circle x² + y² = 20 and the line y = 2x intersect at two points. Which of the following is one of them?
- A. (2, 4)Correct
- B. (4, 2)
- C. (2, 2)
- D. (−4, 2)
Answer: A. (2, 4)
Substitute y = 2x: x² + 4x² = 20, so x² = 4 and x = ±2. Then y = ±4: (2, 4) and (−2, −4).
Why the other answers are wrong
- B. (4, 2)
- (4, 2) is on the circle but not on y = 2x (2 ≠ 8).
- C. (2, 2)
- (2, 2) is on neither: 8 ≠ 20 and 2 ≠ 4.
- D. (−4, 2)
- (−4, 2) is on the circle but the line gives y = −8.
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