Question

Let AB be a chord of the circle x2 + y2 = subtending a
right angle at the centre. Then the locus of the centroid of
the triangle PAB as P moves on the circle is: (2001)
(a) a parabola
(b) a circle
(c) an ellipse
(d) a pair of straight lines.the triangle pqr is inscribed in the circle X square + Y square = ​

Answer 1

Answer:

A circle

Step-by-step explanation:

A{rcos(θ+900),rsin(θ+900)}  

=A(−rsinθ,rcosθ)

θ=0

B(r,0),A(0,r)

Contract of∠PABis(α,β)

α=r+0+rcosθ3=3α−r=rcosθ−(1)

β=0+r+rsinθ3=3β−r=rsinθ−(2) (3α−r)2+(3β−r)2=r2cos2θ+r2sin2θ=r2

(α−r3)2+(β−r3)2=(r3)2

(r3,r3),(r3)

option b is correct.