Question Number 157984 by cherokeesay last updated on 30/Oct/21 Answered by JDamian last updated on 03/Nov/21 $${Assuming}\:\angle{OAB}\:=\:\angle{ABC}\:=\:\mathrm{90}° \\ $$$${there}\:{is}\:{not}\:{such}\:{solution} \\ $$ Commented by ajfour last…
Question Number 157926 by mr W last updated on 29/Oct/21 $${if}\:{the}\:{line}\:{px}+{qy}={r}\:{tangents}\:{the} \\ $$$${ellipse}\:\frac{{x}^{\mathrm{2}} }{{a}^{\mathrm{2}} }+\frac{{y}^{\mathrm{2}} }{{b}^{\mathrm{2}} }=\mathrm{1},\:{then}\: \\ $$$$\left.\mathrm{1}\right)\:{prove}\:\boldsymbol{{a}}^{\mathrm{2}} \boldsymbol{{p}}^{\mathrm{2}} +\boldsymbol{{b}}^{\mathrm{2}} \boldsymbol{{q}}^{\mathrm{2}} =\boldsymbol{{r}}^{\mathrm{2}} \: \\…
Question Number 26693 by Tinkutara last updated on 28/Dec/17 $${STATEMENT}-\mathrm{1}:\:{The}\:{angle}\:{between} \\ $$$${one}\:{of}\:{the}\:{lines}\:{represented}\:{by}\:{ax}^{\mathrm{2}} \:+ \\ $$$$\mathrm{2}{hxy}\:+\:{by}^{\mathrm{2}} \:=\:\mathrm{0}\:{and}\:{one}\:{of}\:{the}\:{lines} \\ $$$${represented}\:{by}\:\left({a}\:+\:\mathrm{2008}\right){x}^{\mathrm{2}} \:+\:\mathrm{2}{hxy} \\ $$$$+\:\left({b}\:+\:\mathrm{2008}\right){y}^{\mathrm{2}} \:=\:\mathrm{0}\:{is}\:{equal}\:{to}\:{angle} \\ $$$${between}\:{other}\:{two}\:{lines}\:{of}\:{the} \\…
Question Number 26449 by Tinkutara last updated on 25/Dec/17 $${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 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…