in this form, multiplying the quadruple (α,β,γ,δ) by a scalar produces a different quadruple that represents the same circle; thus, these quadruples may be considered to be homogeneous coordinates for the space of circles. straight lines may also be represented with an equation of this type in which α = 0 and should be thought of as being a degenerate form of a circle. when α ≠ 0, we may solve for "p" = β/α, "q" = γ/α, and "r" =√("p" + "q" − δ/α); note, however, that the latter formula may give "r" = 0 (in which case the circle degenerates to a point) or "r" equal to an imaginary number (in which case the quadruple (α,β,γ,δ) is said to represent an "imaginary circle").