WBJEE 2012 Math Solved Paper

Since, join of (2, 0) and (0, 3) subtends 90° at (0, 0).
⇒ It is a diameter
∴ Equation is
(x−2)(x−0)+(y−0)(y−3)=0
x2+y2−2x−3y=0
(2k, 3k) lies on it
⇒4k2+9k2−4k−9k=0
⇒13k2=13k
⇒k=1
Since, k ≠ 0 otherwise (2k, 3k) will be (0, 0).