The locus of a point refers to the set of all points that satisfies a given condition or set of conditions. In this case, the condition is that the point is equidistant from a fixed point (3,-1).
To find the equation, you first need to determine the distance formula between the point and the fixed point. This can be done using the Pythagorean theorem. Then, set the distance formula equal to a variable, such as d, and solve for x and y. This will give you the equation for the locus of the point.
The equation represents all the points that are equidistant from the fixed point. This means that any point on this locus will have the same distance from the fixed point as any other point on the locus.
Yes, the equation can be written in different forms depending on the given conditions. For example, if the fixed point is at the origin (0,0), the equation can be simplified to only include the distance formula. If the fixed point is not at the origin, the equation will include both the distance formula and the coordinates of the fixed point.
The locus of a point can be graphed by plotting points that satisfy the given condition, which in this case is being equidistant from the fixed point. This will result in a specific shape, such as a circle, ellipse, or parabola. Alternatively, the equation for the locus of a point can also be plugged into a graphing calculator or software to generate a visual representation.