Menu Close

Category: Coordinate Geometry

z-0-10-cos-3-piz-3-

Question Number 96907 by bemath last updated on 05/Jun/20 $$\underset{\mathrm{z}\:=\:\mathrm{0}} {\overset{\mathrm{10}} {\sum}}\:\mathrm{cos}\:^{\mathrm{3}} \left(\frac{\pi\mathrm{z}}{\mathrm{3}}\right)\:=\:? \\ $$ Commented by john santu last updated on 05/Jun/20 $$\mathrm{cos}\:\mathrm{3x}\:=\:\mathrm{4cos}\:^{\mathrm{3}} \mathrm{x}−\mathrm{3cos}\:\mathrm{x}…

A-point-moves-in-xy-plane-such-that-sum-of-its-distance-from-two-mutually-perpendicular-lines-is-always-3-The-area-encloded-by-the-locus-of-the-point-is-

Question Number 31371 by momo last updated on 07/Mar/18 $${A}\:{point}\:{moves}\:{in}\:{xy}\:{plane}\:{such}\: \\ $$$${that}\:{sum}\:{of}\:{its}\:{distance}\:{from}\:{two}\: \\ $$$${mutually}\:{perpendicular}\:{lines}\:{is} \\ $$$${always}\:\mathrm{3}.{The}\:{area}\:{encloded}\:{by} \\ $$$${the}\:{locus}\:{of}\:{the}\:{point}\:{is} \\ $$ Answered by ajfour last updated…

Question-162309

Question Number 162309 by Mathematification last updated on 28/Dec/21 Commented by mr W last updated on 28/Dec/21 $${it}\:{seems}\:{that}\:{you}\:{and}\:{ms}.\:{tawa}\:{are} \\ $$$${visiting}\:{the}\:{same}\:{college},\:{since}\:{your} \\ $$$${questions}\:{seem}\:{to}\:{be}\:{from}\:{the}\:{same} \\ $$$${source}\:\left({or}\:{teacher}\right). \\…

if-point-of-intersection-of-curves-C-1-x-2-4y-2-2xy-9x-3-and-C-2-2x-2-3y-2-4xy-3x-1-subtends-a-right-angle-at-origin-the-value-of-is-

Question Number 31147 by momo last updated on 03/Mar/18 $${if}\:{point}\:{of}\:{intersection}\:{of}\:{curves} \\ $$$${C}_{\mathrm{1}} =\lambda{x}^{\mathrm{2}} +\mathrm{4}{y}^{\mathrm{2}} −\mathrm{2}{xy}−\mathrm{9}{x}+\mathrm{3}\:{and} \\ $$$${C}_{\mathrm{2}} =\mathrm{2}{x}^{\mathrm{2}} +\mathrm{3}{y}^{\mathrm{2}} −\mathrm{4}{xy}+\mathrm{3}{x}−\mathrm{1}\: \\ $$$${subtends}\:{a}\:{right}\:{angle}\:{at}\:{origin}\:{the} \\ $$$${value}\:{of}\:\lambda\:{is}? \\…

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}…