CircleMedium
Question
Let AB be a chord of the circle x2 + y2 = r2 subtending a right angle at the centre. Then the locus of the centroid of the triangle PAS as P moves on the circle is
Options
A.a parabola
B.a circle
C.an ellipse
D.a pair of straight lines
Solution
Choosing OA as x-axis,A = (r, 0), B = (0, r) and any point P on the circle is (r cos θ, r sin θ)
If the centroid of ᐃPAB, the
3x = r cos θ + r + 0
and 3y = r sin θ + 0 + r
∴ (3x - r)2 + (3y - r)2 = r2
Hence, locus of P is a circle.
Create a free account to view solution
View Solution FreeMore Circle Questions
The locus of the mid-points of the chords of the circle x2 + y2 - 2x - 4y - 11 = 0 which subtend 60o at the centre is -...Lines L1 : x + y = 2 and L2 : y -(2 + √3)x + (1 + √3) = 0 intersect circle S1 = 0 (radius r) at A,B and A,C ...The equation to the circle whose radius is 4 and which touches the negative x-axis at a distance 3 units from the origin...Find the co-ordinates of a point p on line x + y = _ 13, nearest to the circle x2 + y2 + 4x + 6y _ 5 = 0...The locus of the point of intersection of the tangent to the circle $x^{2} + y^{2} = a^{2}$, which include an angle of $...