Julia S. answered • 07/25/21

Calculus Made Manageable

Given the equation (x-10)^{2} + y^{2} = 25, we will need the parametrization equations for circles not centered about the origin:

x = h + rcos(θ)

y = k + rsin(θ)

in which (h,k) is the center of the circle and r is the radius. The center of our circle is at (10,0) so we plug this in for (h,k), and our radius is √25 = 5. Our equations are then

x = 10 + 5cos(θ)

y = 5sin(θ)

for all θ such that 0 ≤ θ ≤ 2π

Julia S.

I reread the problem (I think I got ahead of myself). It requests that you start at (5,0) and move clockwise for 2 theta. In order to start at theta = 0 at the point (5,0), the equation for x would be: x = 5cos(theta) This gives you a value of x = 5 for theta = 0. The original equation works only if you start at (15,0). Please try that and let me know how it goes!07/25/21

Chris N.

the answer is x=10-5cos(theta). Thanks for the help07/26/21

Julia S.

Gotcha - I apologize I couldn’t get you there.07/26/21

Chris N.

I tried that before and it says the equation for x is wrong. "Your second answer is correct, but your first answer is incorrect. The equation of a circle with radius r and center (h,k) is (x-h)^2 + (y-k)^2 = r^2. Determine the relationship between x and y in terms of theta. Use this relationship to write the equation of the circle in terms of x and theta, and then in terms of y and theta in order to find the parametric equations for the particle's motion."07/25/21