Let q> 1. A circle in R is defined to be the set of all points in some two-dimensional affine subspace of Rª that are a fixed positive distance from some fixed point in that affine subspace. The fixed positive distance is the radius of the circle and the fixed point is its center. Let Y, Z₁, and Z2 be members of Rª and suppose that Z₁ and Z₂ have the same norm and are perpendicular to each other. Let F(t) = Y + Z₁ cost + Z₂ sint, 0≤t<2π. Prove that the image of F is a circle by first showing that every member of the image of F is on some circle and then showing that every member of that circle belongs to the image of F. What are the center and radius of the circle?

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