Question

Find the slope of the tangent and the normal to the following curve at the indicted point  xy = 6 at (1, 6) ?

Answer 1

\[ xy = 6\]

\[\text { On differentiating both sides w.r.t. x, we get }\]

\[x\frac{dy}{dx} + y = 0\]

\[ \Rightarrow x\frac{dy}{dx} = - y\]

\[ \Rightarrow \frac{dy}{dx} = \frac{- y}{x}\]

\[\text { Now,} \]

\[\text { Slope of the tangent }= \left( \frac{dy}{dx} \right)_\left( 1, 6 \right) =\frac{- y}{x}=\frac{- 6}{1}=-6\]

\[\text{ Slope of the normal }=\frac{- 1}{\left( \frac{dy}{dx} \right)_\left( 1, 6 \right)}=\frac{- 1}{- 6}=\frac{1}{6}\]