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AJ Bentley said:All you have to do is to find the position of the ring in terms of r and θ.
It's easy to get r in terms of t and also θ in terms of t.
That gives you two formulae - you just have to eliminate 't' between them.
A locus in polar form refers to a set of points that satisfy a certain condition or equation, where the points are represented in polar coordinates (r,θ). It is the path traced by a point as it moves according to a specific rule or relationship.
To find the locus of a point in polar form, you need to identify the relationship between the polar coordinates (r,θ). This relationship can be expressed as an equation, and the set of points that satisfy this equation will be the locus of the point.
Sure, let's say we have the equation r = 3cos(θ). This represents a circle with a radius of 3 centered at the origin. Any point on this circle will satisfy the equation, and therefore, the locus of the point will be this circle.
Finding the locus of a point in polar form can help us understand the relationship between the polar coordinates and the geometry of the points. It can also be useful in solving problems involving motion or curves in polar coordinates.
Yes, there are a few special cases to consider when finding the locus of a point in polar form. These include when the equation involves trigonometric functions (such as sine or cosine), or when the locus is a straight line (which occurs when the equation involves only one variable, either r or θ).