SOLUTION: SP)eccentricity of a conic is defined as how the curve deviates from circular shape. i have understood that's why eccentricity of circle is 0. but we know another definition of ecc

Algebra ->  Quadratic-relations-and-conic-sections -> SOLUTION: SP)eccentricity of a conic is defined as how the curve deviates from circular shape. i have understood that's why eccentricity of circle is 0. but we know another definition of ecc      Log On


   

Question 980712: SP)eccentricity of a conic is defined as how the curve deviates from circular shape. i have understood that's why eccentricity of circle is 0. but we know another definition of eccentricity that is ratio of distance between (point on a locus of conic and focus) and between( point on a locus and directrix) therefore if P(x,y) is a point on locus and S the focus and MZ the directrix so, e=SP/PM . FOR a circle focus is the centre of the circle. if i draw a line beside the circle and imagine it as a directrix , therefore apply e=SP/PM , then the ratio is not 0 . so how eccentricity of circle be 0 in last case ? please explain
Answer by macston(5194) About Me  (Show Source):
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Mathematics sort of cheats on this one, and defines the directrix of a circle as "the line at infinity", meaning the line is an infinite distance from the circle. Dividing a fixed number (focus to circle, or radius) by infinity is "approaching zero". Draw your imaginary directrix an imagined infinity from your circle, and while the ratio e becomes zero for practical purposes, it raises more questions for math theorists to ponder, and may raise questions from you that can be answered more clearly.