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Please refer to the following picture.

enter image description here

A tangent is a line that touches the curve at only one point.

A normal is a line perpendicular to the tangent. Is that the definition of a normal?

Or is the definition of a normal a line that is perpendicular to the tangent at the point where it touches the curve?

Because if the first definition is correct, then can't the line $N_2$ be a normal as well? We know $N_1$ is a normal. But what about $N_2$?

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  • $\begingroup$ A tangent is a line that touches the curve at only one point. This is a very awkward definition (and certainly doesn't agree with the most spread definition of a tangent). $\endgroup$ – gniourf_gniourf Dec 22 '16 at 12:10
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Yes both N1 and N2 can be normals as both lines are perpendicular to the line of the tangent.

Just a quick tip:

The gradient of a normal is always the negative reciprocal of the gradient of the tangent for example.

If the gradient of the tangent is 3 then the gradient of the normal (the negative reciprocal) is -1/3.

To check that this is correct both gradients mutiplied together should give -1.

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