1. Tangents and Normals
by M. Bourne
We often need to find tangents and normals to curves when we are analysing forces acting on a moving body.
A tangent to a curve is a line that touches the curve at one point and has the same slope as the curve at that point.
A normal to a curve is a line perpendicular to a tangent to the curve.
Note 1: As we
discussed before (in Slope of a Tangent to a Curve), we can find the slope of a tangent at any point (x, y) using
.
Note 2: To find the equation of a normal, recall the condition for perpendicularity:
m1 × m2 = -1
Examples:
1. Find the gradient of
(i) the tangent (ii) the normal
to the curve y = x3 - 2x2 + 5 at the point (2,5)
2. Find the equation of the normal in the above example.
Need Graph Paper?
3. Sketch the curve and the normal in the above example.
Let's first see how it looks in LiveMath...
Now for the normal answer:
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