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Category: Coordinate Geometry

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-

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…

Question-199817

Question Number 199817 by ajfour last updated on 09/Nov/23 Answered by ajfour last updated on 09/Nov/23 $$\left\{{a}^{\mathrm{2}} +\frac{\mathrm{1}}{\mathrm{4}}\left(\mathrm{1}−\mathrm{tan}\:^{\mathrm{2}} \theta\right)−\frac{\mathrm{sin}\:\theta}{\mathrm{2}\left(\mathrm{1}+\mathrm{sin}\:\theta\right)}\right\}^{\mathrm{2}} \\ $$$$\:\:\:={a}\left\{{a}+\frac{\mathrm{sin}\:\theta}{\mathrm{2cos}\:\theta\left(\mathrm{1}+\mathrm{sin}\:\theta\right)}\right\} \\ $$$${b}=\frac{\mathrm{sin}\:\theta}{\mathrm{2cos}\:\theta\left(\mathrm{1}+\mathrm{sin}\:\theta\right)} \\ $$…

Given-Fibonacci-series-F-1-F-2-1-and-F-n-2-F-n-1-F-n-for-n-gt-0-Find-the-remainder-F-2022-divides-by-5-

Question Number 199625 by cortano12 last updated on 06/Nov/23 $$\mathrm{Given}\:\mathrm{Fibonacci}\:\mathrm{series}\: \\ $$$$\:\mathrm{F}_{\mathrm{1}} =\mathrm{F}_{\mathrm{2}} =\:\mathrm{1}\:\mathrm{and}\:\mathrm{F}_{\mathrm{n}+\mathrm{2}} =\:\mathrm{F}_{\mathrm{n}+\mathrm{1}} +\mathrm{F}_{\mathrm{n}} \\ $$$$\:\mathrm{for}\:\mathrm{n}>\mathrm{0}.\:\mathrm{Find}\:\mathrm{the}\:\mathrm{remainder}\: \\ $$$$\:\mathrm{F}_{\mathrm{2022}} \:\mathrm{divides}\:\mathrm{by}\:\mathrm{5}\: \\ $$ Answered by…