trajectory/path of an ellipse

a particle describes a path with position vector
r=acos(wt)i+bsin(wt)j

show that the path is an ellipse...
x² /a² +y² /b² =1

i know that r=magnitude of r x unit vector of r,
should this help?

any hints welcome!!

Reply 1

the bear

realicetic

a particle describes a path with position vector
r=acos(ωt)i +bsin(ωt)j

show that the path is an ellipse...
x² /a² +y² /b² =1

i know that r=magnitude of r x unit vector of r,
should this help?

any hints welcome!!

the x component of the particle's position is acos(wt) and the y component is
bsin(wt)

so x² = a²cos²ωt and y² = b²sin²ωt

so x²/a² = cos²ωt and y²/b² = sin²ωt

so x²/a² + y²/b² = cos²ωt + sin²ωt

so x²/a² + y²/b² = 1