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Category: Coordinate Geometry

find-the-equation-of-the-2D-curve-such-that-the-lines-x-t-y-a-t-1-are-always-tangent-to-the-curve-given-a-is-a-positive-real-constant-and-t-is-a-parameter-0-lt-t-lt-a-

Question Number 34326 by 33 last updated on 04/May/18 $${find}\:{the}\:{equation}\:{of}\:{the}\:\mathrm{2}{D} \\ $$$${curve}\:{such}\:{that}\:{the}\:{lines} \\ $$$$\:\frac{{x}}{{t}}\:+\:\frac{{y}}{\left({a}−{t}\right)\:}\:=\:\mathrm{1} \\ $$$$\:{are}\:{always}\:{tangent}\:{to} \\ $$$${the}\:{curve}. \\ $$$${given}\:'{a}'\:\:{is}\:{a}\:{positive}\:{real} \\ $$$${constant}\:{and}\:'{t}'\:{is}\:{a} \\ $$$${parameter}.\:\left(\:\mathrm{0}\:<\:{t}\:<\:{a}\:\right) \\…

Question-165272

Question Number 165272 by cortano1 last updated on 28/Jan/22 Answered by ajfour last updated on 28/Jan/22 $$\mathrm{2}{a}=\mathrm{10}{cm} \\ $$$${a}^{\mathrm{2}} =\left(\mathrm{2}{r}−\mathrm{2}{a}\right)\left(\mathrm{2}{a}\right) \\ $$$${r}=\frac{\mathrm{5}{a}}{\mathrm{4}}=\frac{\mathrm{5}}{\mathrm{8}}\left(\mathrm{10}{cm}\right)=\mathrm{6}.\mathrm{25}{cm} \\ $$ Answered…

Question-165024

Question Number 165024 by cortano1 last updated on 25/Jan/22 Commented by cortano1 last updated on 25/Jan/22 $$\:{find}\:{a}. \\ $$$$\left({A}\right)\mathrm{2}\sqrt{\mathrm{46}}\:\:\:\:\:\:\:\left({C}\right)\mathrm{12} \\ $$$$\left({B}\right)\:\mathrm{2}\sqrt{\mathrm{42}}\:\:\:\:\:\:\:\left({D}\right)\:\mathrm{2}\sqrt{\mathrm{39}} \\ $$ Commented by…

Question-98907

Question Number 98907 by Ramajunan last updated on 17/Jun/20 Answered by mr W last updated on 17/Jun/20 $$\frac{\left(\mathrm{5}+{x}\right)^{\mathrm{2}} +{x}^{\mathrm{2}} −\mathrm{7}^{\mathrm{2}} }{\mathrm{2}\left(\mathrm{5}+{x}\right){x}}=−\frac{\mathrm{5}^{\mathrm{2}} +{x}^{\mathrm{2}} −\mathrm{7}^{\mathrm{2}} }{\mathrm{2}×\mathrm{5}{x}} \\…