Question

If a circle of constant radius 3k passes through the origin ‘O’ and meets co-ordinate axes at A and B then the locus of the centroid of the triangle OAB is

• A. $x^2+y^2=(2k{)}^2$
• B. $x^2+y^2=(3k{)}^2$
• C. $x^2+y^2=(4k{)}^2$
• D. $x^2+y^2=(6k{)}^2$

Answer 1

The correct option is A $x^2+y^2=(2k{)}^2$

A(a, 0) B(0, b) O(0, 0)
$(x,y)=(\frac{a}{3},\frac{b}{3})$
AB =6k
$a^2+b^2=36k^2$ i.e $x^2+y^2=4k^2$