Question # 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 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} )

Solution

( 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)