Question-221413

Question Number 221413 by BHOOPENDRA last updated on 04/Jun/25

Answered by mr W last updated on 05/Jun/25

x=4 cos θ y=2 sin θ x+y=2(2 cos θ+sin θ)=2(√5) sin (θ+tan^(−1) 2) (x+y)_(min) =−2(√5) (x+y)_(max) =2(√5)

$${x}=\mathrm{4}\:\mathrm{cos}\:\theta \\ $$$${y}=\mathrm{2}\:\mathrm{sin}\:\theta \\ $$$${x}+{y}=\mathrm{2}\left(\mathrm{2}\:\mathrm{cos}\:\theta+\mathrm{sin}\:\theta\right)=\mathrm{2}\sqrt{\mathrm{5}}\:\mathrm{sin}\:\left(\theta+\mathrm{tan}^{−\mathrm{1}} \mathrm{2}\right) \\ $$$$\left({x}+{y}\right)_{{min}} =−\mathrm{2}\sqrt{\mathrm{5}} \\ $$$$\left({x}+{y}\right)_{{max}} =\mathrm{2}\sqrt{\mathrm{5}} \\ $$

Commented by mr W last updated on 05/Jun/25