Question

Statement (1): The point P⁡(𝑥, 𝑦) is at a distance of 6 unit from origin, then P lies in the first quadrant.

Statement (2): Point P can lie in any quadrant.

Options

• Both the statements are true.

• Both the statements are false.

• Statement 1 is true, and statement 2 is false.

• Statement 1 is false, and statement 2 is true.

Answer 1

Statement 1 is false, and statement 2 is true.

Explanation:

• Statement (1): The locus of all points at a fixed distance of 6 units from the origin is a circle given by the equation \[x^2 + y^2 = 6^2 = 36\]. This circle traverses all four quadrants (e.g., \((-6, 0)), ((0, -6)), ((-3\sqrt{2}, -3\sqrt{2})\), etc.). Thus, P does not necessarily lie only in the first quadrant. Hence, Statement (1) is false.
• Statement (2): Since points satisfying \[x^2 + y^2 = 36\] exist with positive and negative combinations of (x) and (y), point P can lie in quadrant I, II, III, or IV. Hence, Statement (2) is true.