CircleHard
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 triangle PQR is inscribed in the circle x2 + y2 = 25 . If Q and R have coordinates (3, 4) and (-4,3) respectively, t...If the equation px2 + (2 − q)xy + 3y2 − 6qx + 30 y + 6q = 0 represents a circle, then the values of p and q ...Consider the hyperbola 3x2 - y2 - 24x + 4y - 4 = 0 -...The locus of the mid point of the focal radii of a variable point moving on the parabola, y2 = 4ax is a parabola whose...The locus of a point which moves such that the tangents from it to the two circle x2 + y2 − 5x − 3 = 0 and 3...