Question

Assertion (A): The point $$P(-2, 4)$$ lies on a circle of radius 6 and centre $$C(3, 5)$$.

Reason (R): $$PC < 6$$.

Options

• Both Assertion (A) and Reason (R) are true and Reason (R) is a correct explanation of Assertion (A).

• Both Assertion (A) and Reason (R) are true but Reason (R) is not a correct explanation of Assertion (A).

• Assertion (A) is true and Reason (R) is false.

• Assertion (A) is false and Reason (R) is true.

Answer 1

Assertion (A) is false and Reason (R) is true.

Explanation:

Step 1 – Assertion: A is false. A point lies on the circle only if its distance from the centre equals the radius. Here: $$ PC = \sqrt{(-2 - 3)^2 + (4 - 5)^2} = \sqrt{26} < 6 $$ Thus, P lies inside the circle, not on it.

Step 2 – Reason: R is true, since $$PC = \sqrt{26}$$ and $$\sqrt{26} < 6$$.