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Category: Coordinate Geometry

A-triangle-has-an-area-of-20-square-units-and-two-vertices-are-3-4-and-2-7-What-is-the-position-of-the-third-vertex-

Question Number 76252 by necxxx last updated on 25/Dec/19 $${A}\:{triangle}\:{has}\:{an}\:{area}\:{of}\:\mathrm{20}\:{square} \\ $$$${units}\:{and}\:{two}\:{vertices}\:{are}\:\left(\mathrm{3},\mathrm{4}\right)\:{and}\:\left(\mathrm{2},\mathrm{7}\right). \\ $$$${What}\:{is}\:{the}\:{position}\:{of}\:{the}\:{third}\:{vertex}? \\ $$ Commented by MJS last updated on 25/Dec/19 $$\mathrm{in}\:\mathrm{words}:\:\mathrm{we}\:\mathrm{know}\:\mathrm{the}\:\mathrm{area}=\frac{\mathrm{side}×\mathrm{height}}{\mathrm{2}} \\…

ind-the-centre-and-radius-of-these-a-6x-2-6y-2-4x-5y-2-0-b-x-2-y-2-6x-8y-1-0-c-3x-2-3y-2-4x-8y-2-0-

Question Number 10660 by okhema last updated on 22/Feb/17 $${ind}\:{the}\:{centre}\:{and}\:{radius}\:{of}\:{these}: \\ $$$$\left({a}\right)\:\mathrm{6}{x}^{\mathrm{2}} +\mathrm{6}{y}^{\mathrm{2}} −\mathrm{4}{x}−\mathrm{5}{y}−\mathrm{2}=\mathrm{0} \\ $$$$\left({b}\right)\:{x}^{\mathrm{2}} +{y}^{\mathrm{2}} +\mathrm{6}{x}+\mathrm{8}{y}−\mathrm{1}=\mathrm{0} \\ $$$$\left({c}\right)\:\mathrm{3}{x}^{\mathrm{2}} +\mathrm{3}{y}^{\mathrm{2}} −\mathrm{4}{x}+\mathrm{8}{y}−\mathrm{2}=\mathrm{0} \\ $$ Answered…

find-the-equation-of-the-circle-with-diameter-AB-where-A-is-at-2-4-and-B-is-at-1-6-

Question Number 10656 by okhema last updated on 22/Feb/17 $${find}\:{the}\:{equation}\:{of}\:{the}\:{circle}\:{with}\:{diameter}\:{AB}\:{where}\:{A}\:{is}\:{at}\:\left(\mathrm{2},\mathrm{4}\right)\:{and}\:{B}\:{is}\:{at}\:\left(−\mathrm{1},\mathrm{6}\right) \\ $$ Answered by FilupS last updated on 22/Feb/17 $$\mathrm{circle}\:\mathrm{centred}\:\mathrm{at}\:\left({a},\:{b}\right)\:\mathrm{with}\:\mathrm{radius}\:{r} \\ $$$${r}=\:\frac{\mathrm{1}}{\mathrm{2}}{AB} \\ $$$$\left({a},\:{b}\right)\:\mathrm{is}\:\mathrm{half}\:\mathrm{way}\:\mathrm{between}\:{A}\:\mathrm{and}\:{B} \\…

Write-in-polar-form-1-3x-y-5-0-2-x-2-x-2-y-2-

Question Number 10129 by Tawakalitu ayo mi last updated on 26/Jan/17 $$\mathrm{Write}\:\mathrm{in}\:\mathrm{polar}\:\mathrm{form}\:. \\ $$$$\left(\mathrm{1}\right)\:\:\mathrm{3x}\:−\:\mathrm{y}\:\:+\:\mathrm{5}\:=\:\mathrm{0} \\ $$$$\left(\mathrm{2}\right)\:\:\mathrm{x}^{\mathrm{2}} \:=\:\sqrt{\mathrm{x}^{\mathrm{2}} \:+\:\mathrm{y}^{\mathrm{2}} } \\ $$ Answered by icyfalcon999 last…

Define-the-inversion-transformation-of-Z-a-ib-where-i-is-imaginary-line-passing-through-the-circle-of-inversion-

Question Number 75580 by lalitchand last updated on 13/Dec/19 $$\mathrm{Define}\:\mathrm{the}\:\mathrm{inversion}\:\mathrm{transformation} \\ $$$$\mathrm{of}\:\mathrm{Z}=\mathrm{a}\:+\:\mathrm{ib}\:\mathrm{where}\:\mathrm{i}\:\mathrm{is}\:\mathrm{imaginary}\:\mathrm{line}\: \\ $$$$\mathrm{passing}\:\mathrm{through}\:\mathrm{the}\:\mathrm{circle}\:\mathrm{of}\:\mathrm{inversion}. \\ $$ Commented by MJS last updated on 13/Dec/19 $$\mathrm{it}'\mathrm{s}\:\mathrm{not}\:\mathrm{clear}.\:\mathrm{i}\:\mathrm{is}\:\mathrm{an}\:\mathrm{imaginary}\:\mathrm{line}? \\…

find-value-in-2-4-13-0-

Question Number 9861 by Raja Naik last updated on 09/Jan/17 $$\mathrm{find}\:\:\lambda\:\mathrm{value}\:\mathrm{in}\:\lambda^{\mathrm{2}} −\mathrm{4}\lambda−\mathrm{13}=\mathrm{0} \\ $$ Answered by FilupSmith last updated on 09/Jan/17 $$\lambda=\frac{\mathrm{4}\pm\sqrt{\mathrm{16}+\mathrm{4}\left(\mathrm{13}\right)}}{\mathrm{2}} \\ $$$$\lambda=\frac{\mathrm{4}\pm\sqrt{\mathrm{68}}}{\mathrm{2}} \\…

Find-the-asymptotes-of-the-hypebola-whose-equation-is-given-by-x-24-y-29-1-

Question Number 9731 by tawakalitu last updated on 29/Dec/16 $$\mathrm{Find}\:\mathrm{the}\:\mathrm{asymptotes}\:\mathrm{of}\:\mathrm{the}\:\mathrm{hypebola}\:\mathrm{whose} \\ $$$$\mathrm{equation}\:\mathrm{is}\:\mathrm{given}\:\mathrm{by}. \\ $$$$\frac{\mathrm{x}}{\mathrm{24}}\:−\:\frac{\mathrm{y}}{\mathrm{29}}\:=\:\mathrm{1} \\ $$ Commented by geovane10math last updated on 29/Dec/16 $$\frac{\mathrm{29}{x}\:−\:\mathrm{24}{y}}{\mathrm{696}}\:=\:\mathrm{1} \\…