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mathmann
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What is the difference between a normal line and a tangent line?
What is the difference between a normal line and a tangent line?
- Thread starter mathmann
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In summary, a normal line and a tangent line both meet at a point on a curve, but differ in their slope or perpendicularity at that point. A tangent line has the same slope as the curve, while a normal line is perpendicular to the curve. Additionally, a tangent line only meets the curve at one point, while a normal line can intersect the curve at multiple points.
- #2
quantumdude
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A line is tangent to a curve if:
1. They both meet at some point.
2. They both have the same slope at that point.
A line is normal to a curve if:
1. They both meet at some point.
2. They are perpendicular to each other at that point.
1. They both meet at some point.
2. They both have the same slope at that point.
A line is normal to a curve if:
1. They both meet at some point.
2. They are perpendicular to each other at that point.
- #3
neutrino
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Tom Mattson said:
Addendum to 1: They meet at only one point.
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Data
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Not quite. The line [itex]y=1[/itex] is tangent to the curve [itex]y=\sin{x}[/itex], but they intersect each other at infinitely many points!neutrino said:
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neutrino
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- #6
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Yes, they do! The article on "tangent line" gets it right, however 
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.FAQ: What is the difference between a normal line and a tangent line?
What is a normal line?
A normal line is a straight line that is perpendicular to a curve at a specific point. It intersects the curve at a 90-degree angle and is used to find the slope of the curve at that point.
What is a tangent line?
A tangent line is a straight line that touches a curve at a specific point. It intersects the curve at only one point and has the same slope as the curve at that point. It is used to approximate the curve at that point.
How are normal lines and tangent lines different?
The main difference between normal lines and tangent lines is that normal lines are perpendicular to a curve while tangent lines only touch the curve at a single point. Additionally, normal lines are used to find the slope of the curve, while tangent lines are used to approximate the curve at a specific point.
When are normal lines and tangent lines used?
Normal lines and tangent lines are commonly used in calculus to find the slope of a curve at a specific point. Normal lines are also used to calculate the rate of change of a function, while tangent lines are used to estimate the behavior of a function near a specific point.
Can normal lines and tangent lines be parallel?
No, normal lines and tangent lines cannot be parallel because a normal line is always perpendicular to the curve at a specific point, while a tangent line only touches the curve at one point and has the same slope as the curve at that point. Therefore, they can never be parallel to each other.