InterviewSolution
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InterviewSolution
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If `x=a((1+t^2)/(1-t^2))`and `y=(2t)/(1-t^2)`, find `(dy)/(dx)` |
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Answer» We have `x=a[-1+(2)/((1-t^(2)))]=1[-1+2(1-t^(2))^(-1)]` `rArr (dx)/(dt)=a[0+2(-1)(1-t^(2))^(-2)(-2t)]=axx(4t)/((1-t^(2))^(2))=(4at)/((1-t^(2))^(2)).` And, `y=(2t)/((1-t^(2)))` `rArr(dy)/(dt)=((1-t^(2)).2-2t(-2t))/((1-t^(2))^(2))(2(1+t^(2)))/((1-t^(2))^(2))` `therefore(dy)/(dx)=((dy//dt))/((dx//dt))={(2(1+t^(2)))/((1-t^(2))^(2))xx((1-t^(2))^(2))/(4at)}=((1+t^(2)))/(2at).` |
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