Rotation of co-ordinate axes:

Suppose that OX, OY be the original axes and OX' and OY' be the new axes which are obtained after rotating OX and OY through an angle θ in anticlockwise direction. Let P be any point in plane having coordinates (x, y) with respect to axes OX and OY and (x', y') with respect to axes OX' and OY'. Then we can say that

x = x' cosθ - y' sinθ, y = x' sinθ + y' cosθ                      ...(1)

and  

x' = x cosθ + y sinθ, y' = - x sinθ + y cosθ         ...(2)

Note: The above transformation can be displaced by a table as follows.

If f(x, y) = 0 is equation of a curve then it is transformed equation is  f( x' cosθ  - y' sinθ , x' sinθ  + y' cosθ ) = 0

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