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Category: Coordinate Geometry

Question-30364

Question Number 30364 by ajfour last updated on 21/Feb/18 Commented by ajfour last updated on 21/Feb/18 $${If}\:{the}\:{parabola}\:{with}\:{focus}\:{F}_{\mathrm{0}} \\ $$$${rolls}\:{on}\:{the}\:{circumference}\:{of} \\ $$$${circle}\:\left({centred}\:{at}\:{origin}\:{and}\right. \\ $$$$\left.{having}\:{radius}\:{r}\right),\:{then}\:{find}\:{the} \\ $$$${locus}\:{of}\:{the}\:{focus}\:{F}\:{of}\:{the}\:{rolling}…

if-plane-3x-4y-tz-2-and-kx-6y-5z-2-0-are-parallel-find-the-value-of-k-and-t-

Question Number 95779 by i jagooll last updated on 27/May/20 $$\mathrm{if}\:\mathrm{plane}\:\mathrm{3x}+\mathrm{4y}+\mathrm{tz}=\mathrm{2}\:\mathrm{and}\: \\ $$$$\mathrm{kx}+\mathrm{6y}+\mathrm{5z}−\mathrm{2}=\mathrm{0}\:\mathrm{are}\:\mathrm{parallel}. \\ $$$$\mathrm{find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\mathrm{k}\:\mathrm{and}\:\mathrm{t}\: \\ $$ Answered by john santu last updated on 27/May/20…

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Question Number 95726 by Rio Michael last updated on 27/May/20 $$\mathrm{th}\:\mathrm{forces}\:{F}_{\mathrm{1}} \:,{F}_{\mathrm{2}} ,{F}_{\mathrm{3}} \:\mathrm{act}\:\mathrm{at}\:\mathrm{points}\:\mathrm{ith}\:\mathrm{position}\:\mathrm{vectors}\:{r}_{\mathrm{1}} ,{r}_{\mathrm{2}} ,{r}_{\mathrm{3}} \:\:\mathrm{where} \\ $$$${F}_{\mathrm{1}} \:=\:\left(\mathrm{4}{i}\:+\:{j}\:+\:\mathrm{2}{k}\right){N}\:\:\:\:\:\:\:{r}_{\mathrm{1}} \:=\:\left(\mathrm{6}{i}\:+\:\mathrm{4}{j}\:+\:{k}\right)\:\mathrm{m} \\ $$$${F}_{\mathrm{2}} \:=\:\left({i}−\mathrm{2}{j}\:+\:{k}\right){N}\:\:\:\:\:\:\:\:\:\:\:{r}_{\mathrm{2}} \:=\:\left({i}\:+\:\mathrm{5}{j}\:−\mathrm{2}{k}\right)\:\mathrm{m}…

find-the-equation-of-the-circle-containing-the-point-2-2-and-passing-throught-the-points-of-intersection-of-the-two-circle-x-2-y-2-3x-2y-4-0-and-x-2-y-2-2x-y-6-0-

Question Number 95639 by i jagooll last updated on 26/May/20 $$\mathrm{find}\:\mathrm{the}\:\mathrm{equation}\:\mathrm{of}\:\mathrm{the}\:\mathrm{circle}\: \\ $$$$\mathrm{containing}\:\mathrm{the}\:\mathrm{point}\:\left(−\mathrm{2},\mathrm{2}\right)\:\mathrm{and} \\ $$$$\mathrm{passing}\:\mathrm{throught}\:\mathrm{the}\:\mathrm{points}\:\mathrm{of}\: \\ $$$$\mathrm{intersection}\:\mathrm{of}\:\mathrm{the}\:\mathrm{two}\:\mathrm{circle}\: \\ $$$$\mathrm{x}^{\mathrm{2}} +\mathrm{y}^{\mathrm{2}} +\mathrm{3x}−\mathrm{2y}−\mathrm{4}=\mathrm{0}\:\mathrm{and}\: \\ $$$$\mathrm{x}^{\mathrm{2}} +\mathrm{y}^{\mathrm{2}} −\mathrm{2x}−\mathrm{y}−\mathrm{6}=\mathrm{0}…

Question-29960

Question Number 29960 by rahul 19 last updated on 14/Feb/18 Answered by ajfour last updated on 15/Feb/18 $$\frac{{x}^{\mathrm{2}} }{{a}^{\mathrm{2}} }+\frac{{y}^{\mathrm{2}} }{{b}^{\mathrm{2}} }=\mathrm{1}\:\Rightarrow\:\:\frac{{x}}{{a}^{\mathrm{2}} }+\frac{{y}}{{b}^{\mathrm{2}} }\left(\frac{{dy}}{{dx}}\right)=\mathrm{0} \\…

Question-161015

Question Number 161015 by mr W last updated on 10/Dec/21 Commented by mr W last updated on 11/Dec/21 $${The}\:{distances}\:{from}\:{the}\:{orthocenter} \\ $$$${to}\:{the}\:{vertexes}\:{of}\:{a}\:{triangle}\:{are} \\ $$$$\boldsymbol{{p}},\:\boldsymbol{{q}},\:\boldsymbol{{r}}\:{respectively}.\:{Find}\:{the}\:{side} \\ $$$${lengthes}\:{of}\:{the}\:{triangle}.…