First slide

Tangents and normals

Question

The slope of the normal to the curve $x = a t^{4}, y = a t^{5}$ at $t = 1$ is

Easy

A

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

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

$\frac{1}{5}$
D

$\frac{- 4}{5}$

Solution

$x = a . t^{4} \Rightarrow \frac{d x}{d t} = 4 a . t^{3}$
$y = a . t^{5} \Rightarrow \frac{d y}{d t} = 5 a . t^{4}$ $\Rightarrow \frac{d y}{d x} = \frac{5}{4} t$

$m = {(\frac{d y}{d x})}_{t = 1} = \frac{5}{4}$

Slope of normal $= \frac{- 4}{5}$

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