Question

The velocity of a particle moving in the x-y plane is given by $\frac{dx}{dt}=8\pi sin2\pi t$ and $\frac{dy}{dt}=5\pi cos2\pi t$ where, t = 0, x = 8 and y = 0, the path of the particle is

• A. a straight line
• B. an ellipse
• C. a circle
• D. a parabola

Answer 1

The correct option is B an ellipse

$\frac{dx}{dt}=8\pi sin2\pi t$

$⟹x=-4cos2\pi t+12$

also $\frac{dy}{dt}=5\pi cos2\pi t$

$⟹y=2.5sin2\pi t$

Hence $\frac{(x-12{)}^2}{4^2}+\frac{y^2}{{2.5}^2}=1$

which is equation of ellipse.