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Question Number 39475 by Raj Singh last updated on 06/Jul/18

Answered by tanmay.chaudhury50@gmail.com last updated on 07/Jul/18

$$calculatiinofslopeat(a,b)w.r.t\frac{x}{a}+\frac{y}{b}=2is$$$$\frac{1}{a}+\frac{\frac{dy}{dx}}{b}=0$$$$\frac{dy}{dx}=-\frac{b}{a}$$$$calculationofslopew.r.t\frac{x^n}{a^n}+\frac{y^n}{b^n}=2$$$$\frac{{nx}^{n-1}}{a^n}+\frac{{ny}^{n-1}\frac{dy}{dx}}{b^n}=0$$$$so{\left(\frac{dy}{dx}\right)}_{(a,b)}$$$$\frac{{na}^{n-1}}{a^n}+\frac{{nb}^{n-1}}{b^n}\times {\left(\frac{dy}{dx}\right)}_{(a,b)}=0$$$${\left(\frac{dy}{dx}\right)}_{(a,b)}\times \frac{{nb}^{n-1}}{b^n}=-\frac{{na}^{n-1}}{a^n}$$$${\left(\frac{dy}{dx}\right)}_{(a,b)}=-\frac{b}{a}$$$$\mathit{s}\mathit{o}\mathit{t}\mathit{h}\mathit{i}\mathit{s}\mathit{t}\mathit{w}\mathit{o}\mathit{c}\mathit{u}\mathit{r}\mathit{v}\mathit{e}\mathit{h}\mathit{a}\mathit{s}\mathit{a}\mathit{c}\mathit{o}\mathit{m}\mathit{m}\mathit{o}\mathit{n}\mathit{t}\mathit{a}\mathit{n}\mathit{g}\mathit{e}\mathit{n}\mathit{t}$$$$\mathit{a}\mathit{t}\mathit{p}\mathit{o}\mathit{i}\mathit{n}\mathit{t}(\mathit{a},\mathit{b})\mathit{t}\mathit{h}\mathit{a}\mathit{t}\mathit{m}\mathit{e}\mathit{a}\mathit{n}\mathit{s}\mathit{t}\mathit{h}\mathit{e}\mathit{y}\mathit{t}\mathit{o}\mathit{u}\mathit{c}\mathit{h}$$$$\mathit{e}\mathit{a}\mathit{c}\mathit{h}\mathit{o}\mathit{t}\mathit{h}\mathit{e}\mathit{r}\mathit{a}\mathit{t}(\mathit{a},\mathit{b})$$$$$$

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