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General
Easy

Question

If t is parameter, A = (aSec t, bTan t) and B = (-aTan t, bSec t), O = (0, 0) then the locus of the centroid of straight capital delta OAB is

  1. 9 x y equals a b    
  2. x y equals 9 a b    
  3. x to the power of 2 end exponent minus 9 y to the power of 2 end exponent equals a to the power of 2 end exponent minus b to the power of 2 end exponent    
  4. x to the power of 2 end exponent minus y to the power of 2 end exponent equals fraction numerator 1 over denominator 9 end fraction open parentheses a to the power of 2 end exponent minus b to the power of 2 end exponent close parentheses    

The correct answer is: 9 x y equals a b


    left parenthesis x comma y right parenthesis equals open parentheses fraction numerator a s e c invisible function application t minus a t a n invisible function application t over denominator 3 end fraction comma fraction numerator b t a n invisible function application t plus b s e c invisible function application t over denominator 3 end fraction close parentheses Eliminate t

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