Mathematics

12th -

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Polar coordinates and curves

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  • 1. Multiple Choice
    3 minutes
    1 pt

    The points A and B have polar coordinates  (6, π3) and (8,π6) \left(6,\ -\frac{\pi}{3}\right)\ and\ \left(8,\frac{\pi}{6}\right)\   respectively.


    The distance AB is

     2132\sqrt{13}  

     (100  483)\sqrt{\left(100\ -\ 48\sqrt{3}\right)}  

    2

    10

  • 2. Multiple Choice
    3 minutes
    1 pt

    OQPR is a rhombus, where Q and R have polar coordiantes (2,2π3) and (2,0)\left(2,\frac{2\pi}{3}\right)\ and\ \left(2,0\right) respectively and O is the pole.  The polar coordinates of P are

     (2,π2)\left(2,\frac{\pi}{2}\right)  

     (2,π3)\left(2,\frac{\pi}{3}\right)  

     (23,5π6)\left(2\sqrt{3},\frac{5\pi}{6}\right)  

     (23,π3)\left(2\sqrt{3},\frac{\pi}{3}\right)  

  • 3. Multiple Choice
    3 minutes
    1 pt

    The polar coordinates of P are (4,π4)\left(4,\frac{\pi}{4}\right)  The pole,O, is the midpoint of the line PQ.

    The Cartesian coordinates of Q are

     (42,42)\left(-4\sqrt{2},-4\sqrt{2}\right)  

     (22,22)\left(-2\sqrt{2},-2\sqrt{2}\right)  

     (23,23)\left(-2\sqrt{3},-2\sqrt{3}\right)  

     (4,3π4)\left(-4,-\frac{3\pi}{4}\right)  

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