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# Tangents and normals

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1. Does the gradient of the tangent and normal multiplied the gradient of the circle always have to equal -1?

Are there any situations where the gradient of the tangent does not have to be multiplied to equal -1?
2. (Original post by Starmock99)
Does the gradient of the tangent and normal multiplied the gradient of the circle always have to equal -1?

Are there any situations where the gradient of the tangent does not have to be multiplied to equal -1?
If we have a point say , then the gradient of the tangent at this point multiplied with the gradient of the normal at this point will ALWAYS = -1
3. Moved to maths.
4. (Original post by Starmock99)
Does the gradient of the tangent and normal multiplied the gradient of the circle always have to equal -1?(...)
The answer is yes and yes again! if the tangent is vertical to the normal and vice versa, the equation of these lines has always to be -1. Look at this picture: click!

As you can see, the y-value of the tangent is -1. The tangent goes always through this point of the y-axis, no matter what the gradient of the tangent is. If it is a different point of the y-axis/another y-value than -1, the gradient of the normal is not vertical to the gradient of the tangent.

That is the reason why the equaiton is always -1.

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