Highly selective Backlog Qs for JEE MainMathematicsStraight Lines
Equation of the locus of the centroid of the triangle whose vertices are a cos k ,   a sin k ,   b sin k , - b cos k and 1 ,   0 , where k is a parameter, is
Options
- A1 - 3 x 2 + 9 y 2 = a 2 + b 2
- B3 x - 1 2 + 9 y 2 = 2 a 2 + 2 b 2
- C3 x + 1 2 + 3 y 2 = a 2 + b 2
- D3 x + 1 2 + 3 y 2 = 3 a 2 + 3 b 2
Correct answer
A. 1 - 3 x 2 + 9 y 2 = a 2 + b 2
Step-by-step solution
Let, the centroid be x ,   y , then x = a cos k + b sin k + 1 3 & y = a sin k - b cos k + 0 3 ⇒   3 x - 1 = a cos k + b sin k     . . . i ⇒   3 y = a sin k - b cos k     . . . ii Square i   &   ii then add we get, ⇒ 3 x - 1 2 + 3 y 2 = a 2 + b 2