Category: Coordinate Geometry

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 $${I}\:{have}\:{posted}\:{an}\:{additional}\:{image}. \\ $$$${I}\:{tried}\:{to}\:{move}\:{and}\:{rotate}\:{the}\:{coordinate} \\ $$$${system},\:{not}\:{the}\:{curve}.\:{The}\:{result} \\ $$$${is}\:{the}\:{same}. \\ $$…

Question Number 26159 by Tinkutara last updated on 21/Dec/17 $$\mathrm{If}\:{x}^{\mathrm{2}} \:+\:{y}^{\mathrm{2}} \:+\:\mathrm{2}{xy}\:+\:\mathrm{2}{x}\:+\:\mathrm{2}{y}\:+\:{k}\:=\:\mathrm{0} \\ $$$$\mathrm{represents}\:\mathrm{pair}\:\mathrm{of}\:\mathrm{straight}\:\mathrm{lines}\:\mathrm{then} \\ $$$$\mathrm{find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:{k}. \\ $$ Answered by ajfour last updated on 21/Dec/17…

Question Number 26021 by ajfour last updated on 17/Dec/17 Commented by ajfour last updated on 17/Dec/17 $${If}\:{a}\:{ray}\:{of}\:{light}\:{from}\:{P}\left({a},{b}\right)\:{has} \\ $$$${to}\:{return}\:{back}\:{to}\:{P}\:{upon}\:{two}\: \\ $$$${reflections},\:{from}\:{parabola}\:{y}={x}^{\mathrm{2}} , \\ $$$${say}\:{at}\:{points}\:{B}\:{and}\:{C}.\:{Then}\:{find} \\…

Question Number 156913 by cortano last updated on 17/Oct/21 Answered by mr W last updated on 17/Oct/21 Commented by cortano last updated on 17/Oct/21 $${blue}\:{length}\:=\:\mathrm{10}\:.\:{yes}\:{thanks}…