What is the standard parametrication of the circle of radius 1 centroid at point into zero zero one in the xy plan is x barabar 1 plus 25 bada hai ya Barabar hai zero ke?

Let the circle of radius 1 with center at (0, 0) be parametrized by x = cos(t) and y = sin(t), where t is the parameter.

To shift the circle's centroid to (1, 0), we can add 1 to the x-coordinate. Thus, the parametrization of the shifted circle becomes:

x = 1 + cos(t)

y = sin(t)

To verify that this is the correct parametrization, we can calculate the centroid of the circle using the formula:

x_bar = (1/(2π)) ∫(a to b) x(t)√(dx/dt)^2 + (dy/dt)^2 dt

y_bar = (1/(2π)) ∫(a to b) y(t)√(dx/dt)^2 + (dy/dt)^2 dt

where a and b are the limits of the parameter t.

For the circle with radius 1 centered at (0, 0), we know that the centroid is at (0, 0). But for the shifted circle with parametrization x = 1 + cos(t) and y = sin(t), we need to verify that the x-coordinate of the centroid is indeed 1.

Using the above formula for x_bar, we have:

x_bar = (1/(2π)) ∫(0 to 2π) (1 + cos(t)) √((-sin(t))^2 + (cos(t))^2) dt

= (1/(2π)) ∫(0 to 2π) (1 + cos(t)) dt

= (1/(2π)) [t + sin(t)](0 to 2π)

= 1

Hence, the x-coordinate of the centroid of the shifted circle is indeed 1, as required.