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Category: Coordinate Geometry

if-the-line-px-qy-r-tangents-the-ellipse-x-2-a-2-y-2-b-2-1-then-1-prove-a-2-p-2-b-2-q-2-r-2-2-find-the-coordinates-of-the-touching-point-

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}} \: \\…

STATEMENT-1-The-angle-between-one-of-the-lines-represented-by-ax-2-2hxy-by-2-0-and-one-of-the-lines-represented-by-a-2008-x-2-2hxy-b-2008-y-2-0-is-equal-to-angle-between-other-t

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} \\…

Transform-the-equation-5x-2-4xy-2y-2-2x-4y-4-0-into-one-without-xy-x-and-y-terms-

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…

Show-that-x-2-4xy-2y-2-6x-12y-15-0-represents-a-pair-of-straight-lines-and-that-these-lines-together-with-the-pair-of-lines-x-2-4xy-2y-2-0-form-a-rhombus-

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-157425

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}…

If-x-2-y-2-2xy-2x-2y-k-0-represents-pair-of-straight-lines-then-find-the-value-of-k-

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…