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Mathematics

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.

  1. Both the statements are true.

  2. Both the statements are false.

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

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

Distance Formula

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Answer

Given, the point P(x, y) is at a distance of 6 unit from origin.

By distance formula,

Distance between two points = (x2−x1)2+(y2−y1)2\sqrt{(x2 - x1)^2 + (y2 - y1)^2}

⇒6=(x−0)2+(y−0)2⇒6=(x)2+(y)2⇒62=x2+y2⇒x2+y2=36.\Rightarrow 6 = \sqrt{(x - 0)^2 + (y - 0)^2}\\[1em] \Rightarrow 6 = \sqrt{(x)^2 + (y)^2}\\[1em] \Rightarrow 6^2 = x^2 + y^2\\[1em] \Rightarrow x^2 + y^2 = 36.

The above equation defines a circle centered at the origin with radius 6. That circle covers all four quadrants, so P can lie anywhere on that circle, not necessarily in the first quadrant.

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

Hence, option 4 is the correct option.

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