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1)

If   Aπ3,Bπ6 are the points on the circle represented in parametric from with centre (0,0)  and radius 12 then the length of the chord AB is 


A) 6(62)

B) 6(63)

C) 2(31)

D) 6(31)

Answer:

Option A

Explanation:

 Parametric  equations  of given circle is x=12cosθ, y=12sinθ

 [ Parametric equation x2+y2=r2 is x=rcosθ,y=rsinθ]

 Now, coordinates  of point A are given by

 x=12cosπ3,y=12sinπ3

   x=12.12,y=12.32

    x=6;y=63

ie,        A=(6,63)

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 and coordinates of point B are given by

    x=12cosπ6,y=12sinπ6

     x=12.32.y=12.12

      x=63,y=6

i.e, B=(63,6)

 Clearly  , length  of chord

AB=6(36)2+(663)2

    =2×62+(31)2

     =62(31)

=6(62)