(Solved): Function and modeling part b please  1. The standard equation of a circle (not centered at the ...

1. The standard equation of a circle (not centered at the origin) with radius \( r \) can be derived from its locus definition: The set of all points, \( P(x, y) \), that are a given distance, \( r \), from a fixed point \( C(h, k) \). a. (2 points) Using the line segment and the fixed point, \( C \), given below, find all the points that are the line segment's distance from the fixed point. b. (5 points) Use the distance formula and the locus definition of a circle to derive the standard equation of a circle.