Question

9. B and C are fixed point having co- ordinates (3, 0) and (-3,0) respectively. If the vertical angle BAC is 90°, then the locus of the centroid of the AABC has the equation (A) x2 + y2 = 1 (B) x2 + y2 = 2 (C) 9(x2 + y2) = 1 (D) 9(x2 + y2) = 4

JEE/Engineering Exams

Maths

Solution

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If angle ( B A C ) is ( 90^{circ} ) then ( A ) is on the circle ( x^{2}+y^{2}=9 ) Centroid ( G ) has coordinates ( left(frac{-3+x_{A}+3}{3}, frac{0+y_{A}+0}{3}right) ) ( equivleft(frac{x_{A}}{3}, frac{y_{A}}{3}right) ) As vertex ( A ) lies on the circle its coordinates satisfy ( x_{A}^{2}+y_{A}^{2}=9 ) which dividing both sides by 9 becomes ( left(frac{x_{A}}{3}right)^{2}+left(frac{y_{A}}{3}right)^{2}=1 ) therefore centroid ( G(x, y) ) will satisfy ( x^{2}+y^{2}=1 )