# How do you find parametric equations for the path of a particle that moves along the #x^2 + (y-3)^2 = 16# once around clockwise, starting at (4,3) 0 ≤ t ≤ 2pi ?

this is a circle of radius 4 centred on (0,3)

we can use polar coordinates but with a twist to reflect the fact that the circle is not centred about the origin

thus we have

it will move clockwise around the circle centre. in polar, angle t is measured clockwise from the x-axis.

By signing up, you agree to our Terms of Service and Privacy Policy

Parametric equations for the path of a particle moving along the given curve can be found using the parametric equations for a circle. The parametric equations for a circle centered at (h, k) with radius r are:

x = h + r * cos(t) y = k + r * sin(t)

For the given curve x^2 + (y - 3)^2 = 16, the center is (h, k) = (0, 3) and the radius is 4. Thus, the parametric equations become:

x = 4 * cos(t) y = 3 + 4 * sin(t)

To start the particle at (4, 3), adjust the initial value of t accordingly:

When t = 0, the particle is at (4, 3), so we use t = 0 as the starting point. When t = 2π, the particle has completed one clockwise revolution around the circle.

Therefore, the parametric equations for the path of the particle are:

x(t) = 4 * cos(t) y(t) = 3 + 4 * sin(t) for 0 ≤ t ≤ 2π.

By signing up, you agree to our Terms of Service and Privacy Policy

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

- What is the arc length of the curve given by #r(t)= (e^tsqrt(2t),e^t,e^(-2t))# on # t in [3,4]#?
- How do you graph parametric equations?
- What is the arc length of the curve given by #r(t)= (-t,2t^2,-t^3)# on # t in [3,4]#?
- How do you use cos(t) and sin(t), with positive coefficients, to parametrize the intersection of the surfaces #x^2+y^2=25# and #z=3x^2#?
- What is the arclength of #f(t) = (tlnt,t/lnt)# on #t in [1,e]#?

- 98% accuracy study help
- Covers math, physics, chemistry, biology, and more
- Step-by-step, in-depth guides
- Readily available 24/7