Advanced MathVery hardNumber of intersection points of a line and a circle
Advanced Math practice question
In the xy-plane, how many points do the graphs of x² + y² = 25 and y = 7 have in common?
- A. NoneCorrect
- B. Exactly one
- C. Exactly two
- D. Infinitely many
Answer: A. None
The circle has radius 5, so no point on it has y = 7 (substituting gives x² = 25 − 49 < 0).
Why the other answers are wrong
- B. Exactly one
- Exactly one would need the line tangent, at y = 5 or y = −5.
- C. Exactly two
- Two would need |y| < 5.
- D. Infinitely many
- A line and a circle never share infinitely many points.
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