Question Number 26411 by Tinkutara last updated on 25/Dec/17 $${Show}\:{that}\:{x}^{\mathrm{2}} \:+\:\mathrm{4}{xy}\:−\:\mathrm{2}{y}^{\mathrm{2}} \:+\:\mathrm{6}{x}\:−\:\mathrm{12}{y} \\ $$$$−\:\mathrm{15}\:=\:\mathrm{0}\:{represents}\:{a}\:{pair}\:{of}\:{straight} \\ $$$${lines}\:{and}\:{that}\:{these}\:{lines}\:{together} \\ $$$${with}\:{the}\:{pair}\:{of}\:{lines}\:{x}^{\mathrm{2}} \:+\:\mathrm{4}{xy}\:−\:\mathrm{2}{y}^{\mathrm{2}} \\ $$$$=\:\mathrm{0}\:{form}\:{a}\:{rhombus}. \\ $$ Answered by…
Question Number 157425 by cortano last updated on 23/Oct/21 Answered by mr W last updated on 23/Oct/21 $${r}^{\mathrm{2}} =\left(\mathrm{8}+{r}\right)^{\mathrm{2}} −\left(\mathrm{7}+{r}\right)^{\mathrm{2}} =\mathrm{15}+\mathrm{2}{r} \\ $$$$\left({r}+\mathrm{3}\right)\left({r}−\mathrm{5}\right)=\mathrm{0} \\ $$$$\Rightarrow{r}=\mathrm{5}…
Question Number 26324 by ajfour last updated on 24/Dec/17 Commented by ajfour last updated on 24/Dec/17 $${Q}.\mathrm{26256}\:\:\:{another}\:{solution}: \\ $$ Commented by mrW1 last updated on…
Question Number 26256 by ajfour last updated on 23/Dec/17 Commented by mrW1 last updated on 23/Dec/17 $${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 26237 by ajfour last updated on 22/Dec/17 Commented by ajfour last updated on 22/Dec/17 $$\left({u},{v}\right)\:{and}\:\left({x},{y}\right)\:{are}\:{equidistant} \\ $$$${from}\:\left({h},{k}\right)\:. \\ $$ Answered by mrW1 last…
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 26148 by ajfour last updated on 21/Dec/17 Commented by ajfour last updated on 21/Dec/17 $${mrW}\mathrm{1}\:{Sir},\:{question}\:{was}\:{for}\:{you}. \\ $$ Commented by mrW1 last updated on…
Question Number 26021 by ajfour last updated on 17/Dec/17 Commented by ajfour last updated on 17/Dec/17 $${If}\:{a}\:{ray}\:{of}\:{light}\:{from}\:{P}\left({a},{b}\right)\:{has} \\ $$$${to}\:{return}\:{back}\:{to}\:{P}\:{upon}\:{two}\: \\ $$$${reflections},\:{from}\:{parabola}\:{y}={x}^{\mathrm{2}} , \\ $$$${say}\:{at}\:{points}\:{B}\:{and}\:{C}.\:{Then}\:{find} \\…
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Question Number 156913 by cortano last updated on 17/Oct/21 Answered by mr W last updated on 17/Oct/21 Commented by cortano last updated on 17/Oct/21 $${blue}\:{length}\:=\:\mathrm{10}\:.\:{yes}\:{thanks}…