The distance from a point to a line or curve is defined as the shortest distance.

Call the equidistant point (x, y) and the closest point on the curve (a, b).

a) The set (locus) of points equidistant from (0, 0) and the line x + y = 1 forms a familiar shape.

Name the shape, and find its equation.(as a relation between x and y or as parametric equations of a)

b) Determine the locus of points equidistant from the origin and the hyperbola x y = 1, x > 0. (as a relation between x and y or as param. eqns of a)

c) Find the locus of points equidistant from the origin and the circle through (1, 1) that's tangent to both axes. (in {x, y} or a form)

Show your steps and reasoning.