KCET2013MathematicsStraight Lines
A ( , ), B ( ,- ) are two points. The locus of the centroid of O A B , where O is the origin, is
Options
- Ax²+y²=3
- B9 x²+9 y²=2
- C2 x²+2 y²=9
- D3 x²+3 y²=2
Correct answer
B. 9 x²+9 y²=2
Step-by-step solution
From figure, we observe that, gathered = 4 A= ( 4 , 4 )= ( 1 2 , 1 2 ) B= ( 4 ,- 4 )= ( 1 2 ,- 1 2 ) gathered and 0=(0,0)= origin Centroid of A B O= 1 2 + 1 2 +0 1 2 - 1 2 +0 3 , 2 3 = ( 2 3 2 , 0 )= ( 2 3 , 0 ) Let (h, k) be centroid of O A B . Then, (h, k)= ( + 3 , - 3 ) + =3 h (i) and - =3 k (ii) Now, on adding Eqs. (i) and (ii) after squaring, we get aligned &(3 h)²+(3 k)²=( + )² & +( - )²=2 & h²+k²= 2 9 aligned Hence, required locus is x²+y²= 2 9 or 9 x²+9 y²=2