AP EAMCET2016MathematicsStraight Lines
Equation of the locus of the centroid of the triangle whose vertices are (a k, a k),(b k,-b k) and (1,0) , where k is a parameter, is
Options
- A(1-3 x)^2+9 y^2=a^2+b^2
- B(3 x-1)^2+9 y^2=2 a^2+2 b^2
- C(3 x+1)^2+(3y)^2=2 a^2+2 b^2
- D(3 x+1)^2+(3y)^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 A, B ad C the vertices of triangle aligned & A =(a k, a k) & B =(b k-b k) & C =(1,0) aligned Let G (x, y) be the centroid, x= a k+b k+1 3 3 x-1=a k+b k ... (i) and y= a k-b k+0 3 and 3 y=a k-b k ... (ii) On squaring and then adding Eqs. (i) and (ii) we get aligned & (3 x-1)^2+3 y^2=a^2 ( ^2 k+ ^2 k )+b^2 ( ^2 k+ ^2 k ) & (3 x-1)^2+9 y^2=a^2+b^2 & (1-3 x)^2+9 y^2=a^2+b^2 aligned