Advanced MathHardSum of x-coordinates where a line meets a circle
Advanced Math practice question
The line y = x + 1 intersects the circle x² + y² = 25 at two points. What is the sum of the x-coordinates of the two points?
Answer: -1
Substitute: x² + (x + 1)² = 25 → 2x² + 2x − 24 = 0 → x² + x − 12 = 0 → (x + 4)(x − 3) = 0. The x-coordinates are −4 and 3, and their sum is −1.
Common wrong answers
- If you answered 1
- 1 is the sum with the sign of 3 − 4 reversed; the roots are −4 and 3.
- If you answered 7
- 7 is the difference 3 − (−4).
- If you answered -12
- −12 is the product of the roots, not the sum.
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