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Category: Coordinate Geometry

Question-123040

Question Number 123040 by ajfour last updated on 22/Nov/20 Commented by ajfour last updated on 22/Nov/20 $${Find}\:{maximum}\:{side}\:{length}\:{of} \\ $$$${equilateral}\:\bigtriangleup{ABC}\:,\:{in}\:{terms}\:{of} \\ $$$${p},\:{q},\:{and}\:{r};\:{the}\:{vertices}\:{of} \\ $$$${which}\:{lie}\:{respectively}\:{on}\:{three} \\ $$$${concentric}\:{circles}\:{of}\:{radii}\:…

Tangents-are-drawn-to-x-2-y-2-16-from-the-point-P-0-h-These-tangents-meet-the-x-axis-at-A-and-B-If-area-of-PAB-is-minimum-then-find-value-of-h-

Question Number 57289 by rahul 19 last updated on 01/Apr/19 $${Tangents}\:{are}\:{drawn}\:{to}\:{x}^{\mathrm{2}} +{y}^{\mathrm{2}} =\mathrm{16}\:{from} \\ $$$${the}\:{point}\:{P}\left(\mathrm{0},{h}\right).{These}\:{tangents}\:{meet} \\ $$$${the}\:{x}−{axis}\:{at}\:{A}\:{and}\:{B}.\:{If}\:{area}\:{of}\:\Delta{PAB} \\ $$$${is}\:{minimum}\:{then}\:{find}\:{value}\:{of}\:{h}\:? \\ $$ Commented by mr W…

Question-57212

Question Number 57212 by Tinkutara last updated on 31/Mar/19 Answered by ajfour last updated on 31/Mar/19 $$\mathrm{a}−\mathrm{2}\sqrt{\mathrm{bc}}=\mathrm{b}+\mathrm{c} \\ $$$$\Rightarrow\:\:\mathrm{c}+\mathrm{2}\sqrt{\mathrm{b}}\sqrt{\mathrm{c}}+\left(\mathrm{b}−\mathrm{a}\right)=\mathrm{0} \\ $$$$\Rightarrow\:\:\sqrt{\mathrm{c}}=\frac{−\mathrm{2}\sqrt{\mathrm{b}}\pm\sqrt{\mathrm{4b}−\mathrm{4}\left(\mathrm{b}−\mathrm{a}\right)}}{\mathrm{2}} \\ $$$$\Rightarrow\:\:\sqrt{\mathrm{c}}=−\sqrt{\mathrm{b}}\pm\sqrt{\mathrm{a}} \\ $$$$\mathrm{but}\:\mathrm{since}\:\sqrt{\mathrm{c}}\:>\mathrm{0}\:\mathrm{so}\:\mathrm{we}\:\mathrm{just}\:\mathrm{consider}…

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}…