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  • Let AB be a chord of the circle subtanding a right angle at the centre, then the lo

Let AB be a chord of the circle x^2+y^2=r^2 subtanding a right angle at the centre, then the locus of the centroid of the triangle PAB as P moves on the circle is
 

Option: 1

a parabola


Option: 2

a circle


Option: 3

an ellipse


Option: 4

a pair of straight line


Answers (1)

best_answer

\\Let \: P \equiv(r \cos \theta, r \sin \theta)\\ \\Centroid \: of \triangle P A B\: is

G\left(\frac{r+0+r \cos \theta}{3}, \frac{0+r+r \sin \theta}{3}\right)

Let,

x=\frac{r+r \cos \theta}{3} \Rightarrow 3 x-r=r \cos \theta\: \: \: \: \: \: \: ...(i)

and,

y=\frac{r+r \sin \theta}{3} \Rightarrow 3 y-r=r \sin \theta\: \: \: \: \: \: \: \: \: ...(ii)

Squaring and adding Eqs. (i) and (ii) , we get

(3 x-r)^2+(3 y-r)^2=r^2

Posted by

Rishabh

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