the postion of apoint in xy plane at time t is given by (ucosa.t,usina.-ptsqared)where u,a,p are constants find the equation of locus of the moving point
 

Asked by ramesh | 3rd Jul, 2016, 09:19: PM

Expert Answer:

Since space ‘ straight t ’ space is space straight a space parameter comma space with space changing space values space of space ‘ straight t ’ comma space the space straight x space and space straight y space coordinates space of space the space moving space point space will space change.
But comma space since space both space straight x space and space straight y space are space related space to space the space same space variable space ‘ straight t ’ comma space they space must space be space related space to space each space other. space
This space relation space in space fact space will space be space the space required space equation space to space the space locus space of space the space moving space point.

straight x space equals space ucosa. straight t space space space space space space space space space straight y space equals space usina minus pt squared

rightwards double arrow straight t equals space straight x over ucosa

straight y space equals space usina minus pt squared
Subsituting space value space of space straight x space in space this space we space get

straight y equals usina minus straight p open parentheses straight x over ucosa close parentheses squared
straight y space equals space usina minus open parentheses fraction numerator straight p over denominator straight u squared cos squared straight a end fraction close parentheses straight x squared

This space is space the space required space equation space of space locus space of space the space moving space point.

Answered by Vijaykumar Wani | 5th Jul, 2016, 06:34: PM