Ex 5.6, 1 If x and y are connected parametrically by the equations without eliminating the parameter, Find ๐๐ฆ/๐๐ฅ, x = 2ใ๐๐กใ^2, y = ใ๐๐กใ^4Here
๐๐ฆ/๐๐ฅ = (๐๐ฆ/๐๐ก)/(๐๐ฅ/๐๐ก)
Calculating ๐ ๐/๐ ๐
๐ฆ = ใ๐๐กใ^4
๐๐ฆ/๐๐ก " =" ใ4๐๐กใ^(4 โ1)
"=" ใ4๐๐กใ^3
Calculating ๐ ๐/๐ ๐
๐ฅ = 2ใ๐๐กใ^2
๐๐ฅ/๐๐ก " =" 2 ร 2๐๐ก
"=" 4๐๐ก
Now,
๐๐ฆ/๐๐ฅ = (๐๐ฆ/๐๐ก)/(๐๐ฅ/๐๐ก)
Putting values
๐๐ฆ/๐๐ฅ = (4๐๐ก^3)/4๐๐ก
๐ ๐/๐ ๐ = t2

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Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths and Science at Teachoo.