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  1. r = a sec q \ r =

    \ r cos q = a

    \ x = a which is a straight line parallel to y - axis at a distance 'a' units from the origin.

  2. r = a (1 + cos q) = r = a + a cos q

    \ r. r = ar + ar cos q or r2 - ar cos q = ar

    then (r2 - ar cos q)2 = a2r2

    \ [x2 + y2 - ax]2 = a2 [x2 + y2]

    This is a cardioid.

  3. r = a (1 + sin q ) \ r = a + a sin q

    \ r . r = a.r + a r sin q

    \ r2 - ar sin q = ar

    \ (r2- ar sin q)2 = a2 r2

    \ [x2 + y2 - ay]2 = a2 [x2 + y2 ] which is cordioid

  4. r =

    \ 2r - r cos q = 4

    \ 2r = 4 + r cos q

    \ (2r)2 = ( 4 + r cos q)2 \ 4r2 = ( 4 + r cos q )2

    \ 4 ( x2 + y2 ) = ( 4 + x )2 or 3x2 + 4y2 - 8x -16 = 0

    which is the rectangular form of an ellipse.

Index

7.1 Scalers & Vectors
7.2 Algebra of Vectors
7.3 Representation of a vector in a plane
7.4 Dotor Scalar product
7.5 Polar Co-ordinates
Supplementary Problems

Chapter 8

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