Question Number 32679 by rahul 19 last updated on 31/Mar/18 $${If}\:\mathrm{4}{a}^{\mathrm{2}} −\mathrm{5}{b}^{\mathrm{2}} +\mathrm{6}{a}+\mathrm{1}=\mathrm{0}\:{and}\:{the}\:{line} \\ $$$${ax}+{by}+\mathrm{1}=\mathrm{0}\:{touches}\:{a}\:{fixed}\:{circle} \\ $$$${then}\:{the}\:{correct}\:{statement}\:{is}\:: \\ $$$$\left.\mathrm{1}\right)\:{centre}\:{of}\:{circle}\:{is}\:{at}\:\left(\mathrm{3},\mathrm{0}\right) \\ $$$$\left.\mathrm{2}\right)\:{radius}\:{of}\:{circle}\:{is}\:\sqrt{\mathrm{3}}. \\ $$$$\left.\mathrm{3}\right)\:{circle}\:{passes}\:{through}\:\left(\mathrm{1},\mathrm{0}\right). \\ $$$$\left.\mathrm{4}\right)\:{none}\:{of}\:{these}.…
Question Number 98185 by abdomathmax last updated on 12/Jun/20 $$\mathrm{developp}\:\mathrm{at}\:\mathrm{fourier}\:\mathrm{serie} \\ $$$$\mathrm{g}\left(\mathrm{x}\right)\:=\frac{\mathrm{2}}{\mathrm{3}+\mathrm{sin}^{\mathrm{2}} \mathrm{x}} \\ $$ Answered by mathmax by abdo last updated on 12/Jun/20 $$\mathrm{g}\left(\mathrm{x}\right)\:=\frac{\mathrm{2}}{\mathrm{3}+\mathrm{sin}^{\mathrm{2}}…
Question Number 32508 by Tinkutara last updated on 26/Mar/18 Answered by MJS last updated on 27/Mar/18 $$\mathrm{there}\:\mathrm{are}\:\mathrm{2}\:\mathrm{tangents}\:\mathrm{of}\:\mathrm{different} \\ $$$$\mathrm{lengths}\:\mathrm{but}\:\mathrm{none}\:\mathrm{of}\:\mathrm{these}\:\mathrm{answers} \\ $$$$\mathrm{fit}\:\mathrm{any}\:\mathrm{of}\:\mathrm{them}… \\ $$$$\mathrm{ellipse}:\:{y}=\pm\frac{{b}}{{a}}\sqrt{{a}^{\mathrm{2}} −{x}^{\mathrm{2}} }…
Question Number 32501 by riza kesk last updated on 26/Mar/18 $$\left(\mathrm{x}−\mathrm{2y}+\mathrm{3}\right)^{\mathrm{2}} +\left(\mathrm{3x}+\mathrm{4y}−\mathrm{1}\right)^{\mathrm{2}} =\mathrm{100} \\ $$$$\mathrm{what}\:\mathrm{is}\:\mathrm{the}\:\mathrm{area}\:\mathrm{of}\:\mathrm{the}\:\mathrm{ellipse}? \\ $$ Answered by MJS last updated on 27/Mar/18 $$\mathrm{the}\:\mathrm{center}\:\mathrm{of}…
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Question Number 31846 by momo last updated on 15/Mar/18 $$\mathrm{25}\left[\left({x}−\mathrm{2}\right)^{\mathrm{2}} +\left({y}−\mathrm{3}\right)^{\mathrm{2}} \right]=\left(\mathrm{3}{x}−\mathrm{4}{y}+\mathrm{7}\right)^{\mathrm{2}} \\ $$$${is}\:{the}\:{equation}\:{of}\:{parabola}.{Find} \\ $$$${length}\:{of}\:{latus}\:{rectum} \\ $$ Commented by momo last updated on 16/Mar/18…
Question Number 162860 by Mathematification last updated on 01/Jan/22 Answered by MJS_new last updated on 01/Jan/22 $${f}\left({x}\right)={x}^{\mathrm{4}} −\mathrm{18}{x}^{\mathrm{2}} −{x}+\mathrm{83} \\ $$$${g}\left({x}\right)={c}_{\mathrm{1}} {x}+{c}_{\mathrm{0}} \\ $$$${h}\left({x}\right)={f}\left({x}\right)−{g}\left({x}\right)={x}^{\mathrm{4}} −\mathrm{18}{x}^{\mathrm{2}}…
Question Number 31639 by Tinkutara last updated on 11/Mar/18 Answered by MJS last updated on 11/Mar/18 $${P}\in{par}:\:\begin{pmatrix}{{p}}\\{\frac{{p}^{\mathrm{2}} }{\mathrm{4}}−\frac{{p}}{\mathrm{2}}+\frac{\mathrm{5}}{\mathrm{4}}}\end{pmatrix} \\ $$$${y}'\left({p}\right)=\frac{{p}}{\mathrm{2}}−\frac{\mathrm{1}}{\mathrm{2}}\:\left(={k}\:\mathrm{of}\:\mathrm{tangent}\:\mathrm{in}\:\mathrm{P}\right) \\ $$$${k}\:\mathrm{of}\:\mathrm{normal}\:{n}\:\mathrm{in}\:\mathrm{P}:\:−\left(\frac{{p}}{\mathrm{2}}−\frac{\mathrm{1}}{\mathrm{2}}\right)^{−\mathrm{1}} = \\ $$$$=−\frac{\mathrm{2}}{{p}−\mathrm{1}}…
Question Number 97143 by Ar Brandon last updated on 06/Jun/20 $$\mathrm{Given}\:\mathrm{f}\left(\mathrm{x}\right)=\frac{\mathrm{ax}^{\mathrm{2}} +\mathrm{bx}+\mathrm{c}}{\mathrm{x}}\:\mathrm{and}\:\mathcal{C}_{\mathrm{f}} \:\mathrm{its}\:\mathrm{graph}; \\ $$$$\mathrm{Determine}\:\mathrm{the}\:\mathrm{real}\:\mathrm{numbers}\:\mathrm{a},\:\mathrm{b},\:\mathrm{and}\:\mathrm{c}\:\mathrm{such}\:\mathrm{that} \\ $$$$\mathcal{C}_{\mathrm{f}} \:\mathrm{passes}\:\mathrm{through}\:\mathrm{the}\:\mathrm{points}\:\mathrm{A}\left(\mathrm{1};\mathrm{2}\right);\:\mathrm{B}\left(−\mathrm{4};\mathrm{8}\right)\:\mathrm{and}\:\mathrm{has} \\ $$$$\mathrm{a}\:\mathrm{tangent}\:\mathrm{parallel}\:\mathrm{to}\:\mathrm{the}\:\mathrm{x}−\mathrm{axis}\:\mathrm{at}\:\mathrm{x}=\mathrm{2}. \\ $$ Answered by MJS…