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Category: Coordinate Geometry

Question-199838

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Question Number 199838 by Calculusboy last updated on 10/Nov/23 Answered by Frix last updated on 10/Nov/23 $${y}=\sqrt[{{x}}]{{xy}} \\ $$$${y}={x}^{\frac{\mathrm{1}}{{x}−\mathrm{1}}} \\ $$$$\left({x}+\mathrm{5}\right)^{{x}} =\mathrm{23}{x}+\mathrm{1}+{x}^{\frac{\mathrm{1}}{{x}−\mathrm{1}}} \\ $$$$\mathrm{Trying}\:{x}=\mathrm{1},\:\mathrm{2},\:\mathrm{3} \\…

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Let-C-be-the-circle-with-the-center-2-3-and-radius-5-a-show-that-P-5-7-lies-on-C-and-find-the-equation-of-the-tangent-at-P-b-show-that-the-line-3x-4y-31-0-is-a-tangent-to-C-

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Question Number 199834 by Calculusboy last updated on 10/Nov/23 $$\boldsymbol{{Let}}\:\boldsymbol{{C}}\:\boldsymbol{{be}}\:\boldsymbol{{the}}\:\boldsymbol{{circle}}\:\boldsymbol{{with}}\:\boldsymbol{{the}}\:\boldsymbol{{center}}\:\left(\mathrm{2},\mathrm{3}\right)\:\boldsymbol{{and}}\:\boldsymbol{{radius}}\:\mathrm{5} \\ $$$$\left.\boldsymbol{{a}}\right)\:\boldsymbol{{show}}\:\boldsymbol{{that}}\:\boldsymbol{{P}}\left(\mathrm{5},\mathrm{7}\right)\:\boldsymbol{{lies}}\:\boldsymbol{{on}}\:\boldsymbol{{C}}\:\boldsymbol{{and}}\:\boldsymbol{{find}}\:\boldsymbol{{the}} \\ $$$$\boldsymbol{{equation}}\:\boldsymbol{{of}}\:\boldsymbol{{the}}\:\boldsymbol{{tangent}}\:\boldsymbol{{at}}\:\boldsymbol{{P}} \\ $$$$\left.\boldsymbol{{b}}\right)\:\boldsymbol{{show}}\:\boldsymbol{{that}}\:\boldsymbol{{the}}\:\boldsymbol{{line}}\:\mathrm{3}\boldsymbol{{x}}−\mathrm{4}\boldsymbol{{y}}+\mathrm{31}=\mathrm{0}\:\boldsymbol{{is}}\:\boldsymbol{{a}}\:\boldsymbol{{tangent}}\:\boldsymbol{{to}}\:\boldsymbol{{C}} \\ $$ Commented by Calculusboy last updated on 10/Nov/23…

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