Please write legibly and show all work and steps.

3) Circles across dimensions. (a) Use the definition of a circle to derive the equation of a circle in R2 with center (a, b) and radius, r. (b) Analogously, use the definition of a sphere to derive the equation of a sphere in R' with center (a, b, c) and radius, r. (c) Use an analogous definition of a hypersphere to derive the equation of a hypersphere in with center (a, b, c, d) and radius, r.(d) A sphere is a two-dimensional object in Ro, and a circle is a one-dimensional object in R2. What is the analogous zero-dimensional object in R? Describe algebraically and geometrically what is going on