Category: Coordinate Geometry

Question Number 157981 by zainaltanjung last updated on 30/Oct/21 $$\mathrm{How}\:\mathrm{much}\:\mathrm{the}\:\mathrm{long}\:\mathrm{of}\:\mathrm{the}\:\mathrm{diagonal} \\ $$$$\:\mathrm{space}\:,\:\mathrm{if}\:\:\mathrm{total}\:\mathrm{area}\:\mathrm{of}\:\mathrm{a}\:\mathrm{cube}\:\mathrm{is} \\ $$$$\:\mathrm{216}\:\mathrm{cm}^{\mathrm{2}} . \\ $$ Answered by cherokeesay last updated on 30/Oct/21 $${the}\:{area}\:{of}\:{one}\:{face}\:{of}\:{cube}\::…

Question Number 157926 by mr W last updated on 29/Oct/21 $${if}\:{the}\:{line}\:{px}+{qy}={r}\:{tangents}\:{the} \\ $$$${ellipse}\:\frac{{x}^{\mathrm{2}} }{{a}^{\mathrm{2}} }+\frac{{y}^{\mathrm{2}} }{{b}^{\mathrm{2}} }=\mathrm{1},\:{then}\: \\ $$$$\left.\mathrm{1}\right)\:{prove}\:\boldsymbol{{a}}^{\mathrm{2}} \boldsymbol{{p}}^{\mathrm{2}} +\boldsymbol{{b}}^{\mathrm{2}} \boldsymbol{{q}}^{\mathrm{2}} =\boldsymbol{{r}}^{\mathrm{2}} \: \\…

Question Number 26449 by Tinkutara last updated on 25/Dec/17 $${Transform}\:{the}\:{equation}\:\mathrm{5}{x}^{\mathrm{2}} \:+\:\mathrm{4}{xy} \\ $$$$+\:\mathrm{2}{y}^{\mathrm{2}} \:−\:\mathrm{2}{x}\:+\:\mathrm{4}{y}\:+\:\mathrm{4}\:=\:\mathrm{0}\:{into}\:{one} \\ $$$${without}\:{xy},\:{x}\:{and}\:{y}\:{terms}. \\ $$ Answered by jota@ last updated on 26/Dec/17…

Question Number 157425 by cortano last updated on 23/Oct/21 Answered by mr W last updated on 23/Oct/21 $${r}^{\mathrm{2}} =\left(\mathrm{8}+{r}\right)^{\mathrm{2}} −\left(\mathrm{7}+{r}\right)^{\mathrm{2}} =\mathrm{15}+\mathrm{2}{r} \\ $$$$\left({r}+\mathrm{3}\right)\left({r}−\mathrm{5}\right)=\mathrm{0} \\ $$$$\Rightarrow{r}=\mathrm{5}…

Question Number 26256 by ajfour last updated on 23/Dec/17 Commented by mrW1 last updated on 23/Dec/17 $${I}\:{have}\:{posted}\:{an}\:{additional}\:{image}. \\ $$$${I}\:{tried}\:{to}\:{move}\:{and}\:{rotate}\:{the}\:{coordinate} \\ $$$${system},\:{not}\:{the}\:{curve}.\:{The}\:{result} \\ $$$${is}\:{the}\:{same}. \\ $$…