Category: Geometry

Question Number 78246 by MJS last updated on 15/Jan/20 $$\mathrm{common}\:\mathrm{equation}\:\mathrm{of}\:\mathrm{conic}\:\mathrm{sections} \\ $$$${ax}^{\mathrm{2}} +{bxy}+{cy}^{\mathrm{2}} +{dx}+{ey}+{f}=\mathrm{0} \\ $$$$\mathrm{if}\:{b}\neq\mathrm{0}\:\mathrm{we}\:\mathrm{rotate} \\ $$$$\mathrm{tan}\:\mathrm{2}\alpha\:=\frac{{b}}{{a}−{c}}\:\left[\mathrm{if}\:{a}={c}\:\Rightarrow\:\alpha=\mathrm{45}°\right] \\ $$$$\begin{cases}{{x}={x}'\mathrm{cos}\:\alpha\:−{y}'\mathrm{sin}\:\alpha}\\{{y}={x}'\mathrm{sin}\:\alpha\:+{y}'\mathrm{cos}\:\alpha}\end{cases} \\ $$$$\mathrm{we}\:\mathrm{now}\:\mathrm{have}\:\left[\mathrm{using}\:{x},\:{y}\:\mathrm{again}\:\mathrm{instead}\:\mathrm{of}\:{x}',\:{y}'\right] \\ $$$${Ax}^{\mathrm{2}} +{Cy}^{\mathrm{2}}…

Question Number 78153 by ajfour last updated on 14/Jan/20 Commented by ajfour last updated on 14/Jan/20 $${Find}\:{h}\:{in}\:{terms}\:{of}\:{c}. \\ $$ Answered by mr W last updated…

Question Number 12566 by JAZAR last updated on 25/Apr/17 $${we}\:{give}\:{U}_{\mathrm{1}} ,{U}_{\mathrm{2}} ,{U}_{\mathrm{3}} \:{the}\:{terms}\:{of}\:{a}\:{geometric}\:{sequence} \\ $$$$.{Determine}\:{U}_{\mathrm{1}} ,{U}_{\mathrm{2}} ,{U}_{\mathrm{3}} \:{such}\:{that}\:: \\ $$$$ \\ $$$$\begin{cases}{{U}_{\mathrm{1}} .{U}_{\mathrm{2}} .{U}_{\mathrm{3}} =\mathrm{64}}\\{{U}_{\mathrm{1}}…

Question Number 12534 by JAZAR last updated on 24/Apr/17 $${please}\:{help}\:{me}\:.{How}\:{can}\:{resolve}\:{this}\:{system}? \\ $$$$\left\{_{\left(\mathrm{1}+\sqrt{\mathrm{2}}\right){x}+{y}=\mathrm{1}} ^{{x}^{\mathrm{2}} +{y}^{\mathrm{2}} =\mathrm{1}} \right. \\ $$ Answered by geovane10math last updated on 25/Apr/17…

Question Number 78042 by $@ty@m123 last updated on 13/Jan/20 Answered by mr W last updated on 13/Jan/20 Commented by mr W last updated on 13/Jan/20…