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The-base-of-triangle-passes-through-a-fixed-point-p-a-b-and-its-sides-are-respectively-bisected-at-right-angles-by-the-line-x-y-0-and-x-9y-if-the-locus-of-the-third-vartex-is-a-circle-then-find-its

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Question Number 43005 by mondodotto@gmail.com last updated on 06/Sep/18 $$\mathrm{The}\:\mathrm{base}\:\mathrm{of}\:\mathrm{triangle}\:\mathrm{passes}\:\mathrm{through} \\ $$$$\mathrm{a}\:\mathrm{fixed}\:\mathrm{point}\:\mathrm{p}\left(\mathrm{a},\mathrm{b}\right)\:\mathrm{and}\:\mathrm{its}\:\mathrm{sides} \\ $$$$\mathrm{are}\:\mathrm{respectively}\:\mathrm{bisected}\:\mathrm{at}\:\mathrm{right}\:\mathrm{angles}\: \\ $$$$\mathrm{by}\:\mathrm{the}\:\mathrm{line}\:\mathrm{x}+\mathrm{y}=\mathrm{0}\:\mathrm{and}\:\mathrm{x}=\mathrm{9y} \\ $$$$\mathrm{if}\:\mathrm{the}\:\mathrm{locus}\:\mathrm{of}\:\mathrm{the}\:\mathrm{third}\:\mathrm{vartex}\:\mathrm{is}\:\mathrm{a}\:\mathrm{circle}. \\ $$$$\mathrm{then}\:\mathrm{find}\:\mathrm{its}\:\mathrm{equation}. \\ $$ Commented by mondodotto@gmail.com…

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Question-108498

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Question Number 108498 by mohammad17 last updated on 17/Aug/20 Answered by Aziztisffola last updated on 17/Aug/20 $$\left.\mathrm{1}\right)\:\mathrm{y}=\left(\mathrm{x}+\mathrm{2}\right)^{\mathrm{x}} =\:\mathrm{e}^{\mathrm{xln}\left(\mathrm{x}+\mathrm{2}\right)} \\ $$$$\frac{\mathrm{dy}}{\mathrm{dx}}=\left(\mathrm{ln}\left(\mathrm{x}+\mathrm{2}\right)+\frac{\mathrm{x}}{\mathrm{x}+\mathrm{2}}\right)\left(\mathrm{x}+\mathrm{2}\right)^{\mathrm{x}} \\ $$$$\frac{\mathrm{dy}}{\mathrm{dx}}\left(−\mathrm{1}\right)=−\mathrm{1} \\ $$ Commented…

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