Question

Among the following, the point that does not lie on the circle with centre at origin and radius \(3\) cm is

• A. \((3,0)\)
• B. \((0,-3)\)
• C. \((2,\sqrt{5})\)
• D. \((2,2)\)

Hint:

For a circle centred at the origin: \[ x^2+y^2=r^2. \] Substitute the coordinates of each point. If the equation is satisfied, the point lies on the circle.

Answer 1

The Correct Option is D

Concept: The equation of a circle with centre at the origin and radius \(r\) is \[ \boxed{x^2+y^2=r^2} \] Here, \[ r=3, \] so the equation becomes \[ x^2+y^2=9. \]

Step 1: Check each point.
For \((3,0)\), \[ 3^2+0^2=9. \] Hence, it lies on the circle. For \((0,-3)\), \[ 0^2+(-3)^2=9. \] Hence, it lies on the circle. For \((2,\sqrt5)\), \[ 2^2+(\sqrt5)^2=4+5=9. \] Hence, it lies on the circle. For \((2,2)\), \[ 2^2+2^2=4+4=8\neq9. \] Therefore, it does not lie on the circle.

Step 2: Final conclusion.
The point which does not satisfy \[ x^2+y^2=9 \] is \[ \boxed{(2,2)}. \]