Find the equations of the tangent and the normal to the curve `x y=c^2` at `(c t ,\ c//t)` at the indicated points.

Explanation

`x y=c^{2}`


Differentiating both sides w.r.t.x ,

`x \frac{d y}{d x}+y=0 \Rightarrow \frac{d y}{d x}=\frac{-y}{x}` Given `(x_{1}, y_{1})=(c t, \frac{c}{t})`

Slope of tangent, `m=(\frac{d y}{d x})_{(c t, \frac{c}{t})}=\frac{-\frac{c}{t}}{c t}=\frac{-1}{t^{2}}`

Slope of tangent, `m=(\frac{d y}{d x})_{(c t, \frac{c}{t})}=\frac{-\frac{c}{t}}{c t}=\frac{-1}{t^{2}}`

Equation of tangent is ,

`y-y_{1}=m(x-x_{1}) `

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