Parameterizing a circle means to express the coordinates of points on the circle in terms of one or more parameters, such as the angle or distance from the center. This allows for a more convenient and flexible way to describe the circle's points.
The radius of the circle is 3 units. This means that the distance from the center of the circle to any point on the circle is 3 units.
The center of the circle has coordinates (3,4). This means that the center of the circle is located 3 units to the right and 4 units up from the origin (0,0) on the coordinate plane.
To find the coordinates of a point on the circle, you can use the parametric equations x = 3 + 3cosθ and y = 4 + 3sinθ, where θ is the angle from the positive x-axis to the point on the circle. Simply plug in different values for θ to find the corresponding coordinates of different points on the circle.
Parameterizing a circle allows for a more efficient and versatile way to describe the points on the circle. It also allows for easier calculations and manipulations, as well as the ability to easily plot points on the circle using different values for the parameter.