Question

Locus of centroid of the triangle whose vertices are (acost , asint) , (bsint, - bcost) and ( 1, 0) where t is a parameter , is

(a) (3x + 1) ² + ( 3y)² = a²-b²

(b) (3x - 1)² +( 3y)² = a² - b²

(c) (3x -1)² + (3y)² = a² + b²

(d) (3x +1)² +( 3y)² = a²+b²

Answer 1

Hello !!

Solution

We know that formula of centroid

X = x1 + X2 + X3 /3 , Y = y1 + y2+ y3/3

•°• X = acost + bsint + 1/3 _____(1)

=> acost + bsint = 3X- 1

similarly ,

asint - bcost = 3Y _______(2)

squaring and adding (1) and (2) equation

(3x - 1 ) ² + ( 3y)² = (asint - bcost )² + (acost+ bsint)²


= (3x - 1)² + (3y)² = a² + b² .

Hence , ur option
$\bold{c}$
is correct option

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Hope it helps you !!! #Muskraj❤❤