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Let e>0 be any positive number. Suppose a conic section has eccentricity e, has

ID: 2843595 • Letter: L

Question

Let e>0 be any positive number. Suppose a conic section has eccentricity e, has x = -1 as its directrix, and has (1,0) as its focus. Please refer to the attached picture for the questions.

Let e>0 be any positive number. Suppose a conic section has eccentricity e, has x = -1 as its directrix, and has (1,0) as its focus. Find two (if e 1) or one (if e = 1) x-intercept of this conic section, expressed as a function of e. Express the x coordinate of the center of the conics as a function of e, for e 1. [Remember that the center is the midpoint of the two vertices for both ellipses and hyperbolas Parabolas have no center] Let's call this function H(e). Sketch this function (horizontal axis will be e-axis that shows the eccentricities and the vertical axis will be the location of center.) Find lim H(e). (I put a visual help (an animation) in the blackboard.] [Attach more papers as needed.]

Explanation / Answer

a)

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