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Help with FP3 further coordinate systems question watch

    • Thread Starter

    Could someone explain the answer to part d? I managed the y axis part, but I don't get the inequalities.


    so the two tangent points are on the ellipse one directly above the other. the tangent lines will cross at a point on the x axis ( because the ellipse has the x axis as a line of symmetry ). so the locus will be the part of the x axis outside the ellipse.
    • Community Assistant

    Community Assistant
    (Original post by moz4rt)
    Could someone explain the answer to part d? I managed the y axis part, but I don't get the inequalities.
    As \theta varies, \cos \theta goes between -1 and 1, but since it is in the denominator, the fraction \frac{1}{\cos \theta} has range \leq -1 or  \geq 1. (look at the graph of \sec \theta), and so then since we have |\sec \theta| \geq 1, mult both sides by a and we get that |a\sec \theta| \geq a which implies that  a \sec \theta \leq -a or a \sec \theta \geq a. Since the x-coordinate of R is precisely a \sec \theta, we get the inequalities.
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Updated: March 9, 2018

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