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Category: Coordinate Geometry

dx-a-btanx-

Question Number 189923 by alcohol last updated on 24/Mar/23 $$\int\frac{{dx}}{{a}\:+\:{btanx}} \\ $$ Answered by CElcedricjunior last updated on 24/Mar/23 $$\int\frac{\boldsymbol{{dx}}}{\boldsymbol{{a}}+\boldsymbol{{btanx}}}=\boldsymbol{{k}} \\ $$$$\boldsymbol{{posons}}\:\boldsymbol{{tanx}}=\boldsymbol{{t}}=>\boldsymbol{{dx}}=\frac{\mathrm{1}}{\mathrm{1}+\boldsymbol{{t}}^{\mathrm{2}} }\boldsymbol{{dt}} \\ $$$$\boldsymbol{{k}}=\int\frac{\boldsymbol{{dt}}}{\left(\boldsymbol{{a}}+\boldsymbol{{bt}}\right)\left(\mathrm{1}+\boldsymbol{{t}}^{\mathrm{2}}…

1-determiner-l-aire-de-la-partie-hachuree-SDEB-2-le-raport-R-1-R-2-sachant-que-AB-20-diametre-de-C-CDE-60-OAD-30-AI-EF-

Question Number 189854 by a.lgnaoui last updated on 22/Mar/23 $$\mathrm{1}−{determiner}\:{l}\:{aire}\:{de}\:{la} \\ $$$${partie}\:{hachuree}\left({SDEB}\right) \\ $$$$\mathrm{2}−{le}\:{raport}\:\frac{{R}_{\mathrm{1}} }{{R}_{\mathrm{2}} } \\ $$$${sachant}\:{que}:\:{AB}=\mathrm{20}\left({diametre}\:{de}\:\left({C}\right)\right. \\ $$$$\:\:\measuredangle{CDE}=\mathrm{60}^{°} \:\:\:\measuredangle{OAD}=\mathrm{30}°.\:\:\left[{AI}\mid\mid{EF}\right. \\ $$$$\:\: \\ $$…

A-variable-point-P-x-y-moves-on-the-curve-xy-6-and-R-is-the-point-which-divides-the-straight-line-that-joins-the-points-A-2-0-and-B-0-1-in-the-ratio-3-1-internally-Find-the-locus-of-PR

Question Number 124001 by Don08q last updated on 30/Nov/20 $$\mathrm{A}\:\mathrm{variable}\:\mathrm{point}\:{P}\left({x},\:{y}\right)\:\mathrm{moves}\:\mathrm{on}\:\mathrm{the} \\ $$$$\mathrm{curve}\:\:{xy}\:=\:\mathrm{6}\:\mathrm{and}\:{R}\:\mathrm{is}\:\mathrm{the}\:\mathrm{point}\:\mathrm{which}\: \\ $$$$\mathrm{divides}\:\mathrm{the}\:\mathrm{straight}\:\mathrm{line}\:\mathrm{that}\:\mathrm{joins}\:\mathrm{the} \\ $$$$\mathrm{points}\:{A}\left(−\mathrm{2},\:\mathrm{0}\right)\:\:\mathrm{and}\:\:{B}\left(\mathrm{0},\:−\mathrm{1}\right)\:\mathrm{in}\:\mathrm{the} \\ $$$$\mathrm{ratio}\:\mathrm{3}:\mathrm{1},\:\mathrm{internally}.\:\mathrm{Find}\:\mathrm{the}\:\mathrm{locus}\:\mathrm{of} \\ $$$${PR}. \\ $$ Answered by liberty…

If-parabola-y-x-2-2x-k-touches-the-parabola-y-1-2-x-2-4x-3-then-the-value-of-k-is-a-1-b-2-c-3-d-4-

Question Number 58400 by rahul 19 last updated on 22/Apr/19 $${If}\:{parabola}\:{y}=−{x}^{\mathrm{2}} −\mathrm{2}{x}+{k}\:{touches} \\ $$$${the}\:{parabola}\:{y}=−\frac{\mathrm{1}}{\mathrm{2}}{x}^{\mathrm{2}} −\mathrm{4}{x}+\mathrm{3}\:,\:{then} \\ $$$${the}\:{value}\:{of}\:{k}\:{is}\:? \\ $$$$\left.{a}\left.\right)\left.\:\left.\mathrm{1}\:\:\:\:{b}\right)\mathrm{2}\:\:\:\:\:{c}\right)\mathrm{3}\:\:\:\:\:{d}\right)\mathrm{4} \\ $$ Commented by rahul 19…