Question-95202

Question Number 95202 by mathocean1 last updated on 23/May/20

Commented by PRITHWISH SEN 2 last updated on 24/May/20

x=2(2cos^2 θ−1)−1=2cos2θ−1 ∴(x+1)^2 +(y−2)^2 = 4...(i) it is the equation of a circle with centre at (−1,2) and a radius of 2 units ∴ E be the set of all points satisfing the equation (i) please check.

$$\mathrm{x}=\mathrm{2}\left(\mathrm{2cos}^{\mathrm{2}} \theta−\mathrm{1}\right)−\mathrm{1}=\mathrm{2cos2}\theta−\mathrm{1} \\ $$$$\therefore\left(\mathrm{x}+\mathrm{1}\right)^{\mathrm{2}} +\left(\mathrm{y}−\mathrm{2}\right)^{\mathrm{2}} =\:\mathrm{4}…\left(\mathrm{i}\right) \\ $$$$\boldsymbol{\mathrm{it}}\:\boldsymbol{\mathrm{is}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{equation}}\:\boldsymbol{\mathrm{of}}\:\boldsymbol{\mathrm{a}}\:\boldsymbol{\mathrm{circle}}\:\boldsymbol{\mathrm{with}}\:\boldsymbol{\mathrm{centre}}\:\boldsymbol{\mathrm{at}}\:\left(−\mathrm{1},\mathrm{2}\right) \\ $$$$\boldsymbol{\mathrm{and}}\:\boldsymbol{\mathrm{a}}\:\boldsymbol{\mathrm{radius}}\:\boldsymbol{\mathrm{of}}\:\mathrm{2}\:\boldsymbol{\mathrm{units}} \\ $$$$\therefore\:\mathrm{E}\:\mathrm{be}\:\mathrm{the}\:\mathrm{set}\:\mathrm{of}\:\mathrm{all}\:\mathrm{points}\:\mathrm{satisfing}\:\mathrm{the}\:\mathrm{equation} \\ $$$$\left(\boldsymbol{\mathrm{i}}\right) \\ $$$$\boldsymbol{\mathrm{please}}\:\boldsymbol{\mathrm{check}}. \\ $$

Commented by mathocean1 last updated on 24/May/20