A family of circles has centers along a straight line passing through the origin of an xycoordinate system at a clockwise angle of 45 0 from the x-axis. The radius of each circle is equal to one-half...

A family of circles has centers along a straight line passing through the origin of an xycoordinate system at a clockwise angle of 45⁰
from the x-axis. The radius of each circle is equal to one-half of the distance from the origin to the center of the circle. Determine the envelope for this family of curves.

(a) as a function relating x and y and

(b) in parametric form, with x and y as functions of a parameter.