First slide

Tangents and normals

Question

The slope of the normal to the curve $x = a (θ - \sin θ), y = a (1 - \cos θ)$ at $θ = \frac{π}{2}$ is

Easy

A

0
B

1
C

$- 1$
D

$\frac{1}{\sqrt{2}}$

Solution

$x = a (θ - \sin θ), y = a (1 - \cos θ)$ at $θ = \frac{π}{2}$
Slope of normal ${\frac{- 1}{(\frac{d y}{d x})}}_{θ = \frac{π}{2}} = \frac{- 1}{1} = - 1$

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