question_answer

Locus of centroid of the triangle whose vertices are (b sin t, - b cost) and (1, 0), where t is a parameter, is     AIEEE  Solved  Paper-2003

A) \[{{(3x-1)}^{2}}+{{(3y)}^{2}}={{a}^{2}}-{{b}^{2}}\]

B) \[{{(3x-1)}^{2}}+{{(3y)}^{2}}={{a}^{2}}+{{b}^{2}}\]

C) \[{{(3x+1)}^{2}}+{{(3y)}^{2}}={{a}^{2}}+{{b}^{2}}\]

D) \[{{(3x+1)}^{2}}+{{(3y)}^{2}}={{a}^{2}}-{{b}^{2}}\]

Correct Answer: B

Solution :

Coordinates of the vertices of a triangle are  and (1, 0). So, centroid is                                                        ?. (i) and                                                    ... (ii) On squaring and adding Eqs. (i) and (ii), we get