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Category: Coordinate Geometry

Question-57174

Question Number 57174 by Tinkutara last updated on 31/Mar/19 Answered by ajfour last updated on 31/Mar/19 $$\mathrm{eq}.\:\mathrm{of}\:\mathrm{L} \\ $$$$\mathrm{y}=\mathrm{3}+\mathrm{rsin}\:\theta\:\:,\:\:\mathrm{x}=\mathrm{2}+\mathrm{rcos}\:\theta \\ $$$$\mathrm{Q}\equiv\left(\mathrm{2}+\mathrm{Rcos}\:\theta,\mathrm{3}+\mathrm{Rsin}\:\theta\right)\equiv\left(\mathrm{h},\mathrm{k}\right) \\ $$$$\mathrm{3}+\mathrm{r}_{\mathrm{A}} \mathrm{sin}\:\theta=\mathrm{12}+\mathrm{r}_{\mathrm{A}} \mathrm{cos}\:\theta…

Question-188177

Question Number 188177 by cortano12 last updated on 26/Feb/23 Commented by cortano12 last updated on 26/Feb/23 $$\:\left[\:\mathrm{BCDH}\:\right]\:=\:\mathrm{6m}^{\mathrm{2}} \\ $$$$\:\left[\:\mathrm{ABI}\:\right]\:=\:\mathrm{4m}^{\mathrm{2}} \\ $$$$\:\left[\:\mathrm{DGE}\:\right]\:=\mathrm{2m}^{\mathrm{2}} \\ $$$$\:\mathrm{Find}\:\left[\:\mathrm{AIF}\:\right] \\ $$…

Question-122456

Question Number 122456 by ajfour last updated on 17/Nov/20 Commented by ajfour last updated on 17/Nov/20 $${y}=\mathrm{1}+\frac{{c}}{{x}}\:\:\:\:\:\:\:\:\:\left(\mathrm{0}<{c}<\frac{\mathrm{2}}{\mathrm{3}\sqrt{\mathrm{3}}}\right) \\ $$$${y}={x}^{\mathrm{2}} \\ $$$${both}\:{these}\:{curves}\:{intersect}\:{at} \\ $$$${P},\:{Q},\:{R}\:\:{as}\:{shown};\:\:{find}\:{eq}.\:{of} \\ $$$${circle}\:{through}\:{these}\:{three}\:{points}…

The-shortest-distance-between-the-point-3-2-0-and-the-curve-y-x-x-gt-0-is-

Question Number 56914 by rahul 19 last updated on 26/Mar/19 $${The}\:{shortest}\:{distance}\:{between}\:{the}\:{point} \\ $$$$\left(\frac{\mathrm{3}}{\mathrm{2}},\mathrm{0}\right)\:{and}\:{the}\:{curve}\:{y}=\sqrt{{x}}\:,\left({x}>\mathrm{0}\right)\:{is}\:? \\ $$ Answered by Smail last updated on 26/Mar/19 $${d}=\sqrt{\left({x}_{\mathrm{2}} −{x}_{\mathrm{1}} \right)^{\mathrm{2}}…

Let-the-points-P-x-n-1-y-n-1-Q-x-n-y-n-and-R-x-n-1-y-n-1-lies-on-the-curve-y-f-x-Prove-that-y-n-1-y-n-1-2h-dy-dx-n-

Question Number 122187 by physicstutes last updated on 14/Nov/20 $$\mathrm{Let}\:\mathrm{the}\:\mathrm{points}\:{P}\left({x}_{{n}−\mathrm{1}} ,{y}_{{n}−\mathrm{1}} \right),\:{Q}\left({x}_{{n}} ,{y}_{{n}} \right)\:\mathrm{and}\:{R}\left({x}_{{n}+\mathrm{1}} ,{y}_{{n}+\mathrm{1}} \right)\:\mathrm{lies} \\ $$$$\mathrm{on}\:\mathrm{the}\:\mathrm{curve}\:{y}\:=\:{f}\left({x}\right).\:\mathrm{Prove}\:\mathrm{that}\: \\ $$$$\:\:{y}_{{n}+\mathrm{1}} \approx\:{y}_{{n}−\mathrm{1}} \:+\:\mathrm{2}{h}\:\left(\frac{{dy}}{{dx}}\right)_{{n}} .\: \\ $$…