A partical moves in the x -y plane ...
Question
A partical moves in the x -y plane according to the scheme x=−8 sinrt and y=−2cos^2πt, where t is time. Find the equation of path of the particle.
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A partical moves in the ( x ) -y plane according to the scheme ( x=-8 ) sinrt and ( y=-2 cos ^{2} pi t ), where t is time. Find the equation of path of the particle.
(A) ( y=-2+frac{x^{2}}{32} )
(B) ( y^{2}=-2+frac{x^{2}}{32} )
( (C) x^{2}=-2+frac{y^{2}}{32} )
(D) ( x=-2+frac{y^{2}}{32} )

JEE/Engineering Exams
Physics
Solution
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A partical moves in the x -y plane according to the scheme x=−8 sinrt and y=−2cos^2πt, where t is time. Find the equation of path of the particle.
Fullscreen

( x=-8 sin (pi t) ; y=-2 cos ^{2} pi t )
( Rightarrow sin ^{2}(pi t)=frac{x^{2}}{64} ; cos ^{2} pi t=frac{-y}{2} )
( sin ^{2} pi t+cos ^{2} x=1 Rightarrow frac{x^{2}}{64}-frac{y}{2}=1 )
( Rightarrow frac{y}{2}=frac{x^{2}}{64}-1 Rightarrow y=frac{x^{2}}{32}-2=-2+frac{x^{2}}{32} )
Option (4)

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