First slide

Tangents and normals

Question

The slope of the normal to the curve $x = a t^{3}, y = a t^{4}$ at $t = 1$ is

Moderate

A

$- \frac{1}{2}$
B

$- \frac{2}{3}$
C

$\frac{1}{4}$
D

$\frac{- 3}{4}$

Solution

$x = a t^{3}, y = a t^{4}$ at $t = 1$
$\frac{d y}{d x} = \frac{4 a t^{3}}{3 a t^{2}} = \frac{4}{3} a t t = 1$
Slope of normal $= \frac{- 1}{{(\frac{d y}{d x})}_{t = 1}} = \frac{- 1}{(\frac{4}{3})} = \frac{- 3}{4}$

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