Advanced MathMediumDistance between the points where a horizontal line meets a parabola
Advanced Math practice question
In the xy-plane, the line y = 6 intersects the parabola y = x² − 3 at two points. What is the distance between the two points?
Answer: 6
Set x² − 3 = 6: x² = 9, so x = ±3. The points are (−3, 6) and (3, 6), 6 units apart.
Common wrong answers
- If you answered 3
- 3 is one x-coordinate, or half the distance.
- If you answered 9
- 9 is x², not the distance.
- If you answered 12
- 12 comes from using y = 6 and y = −6 as the two points.
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