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NCERT Class 12 · Ch 1 Exercise 1.1 · Q11

NCERT Class 12 Maths · Chapter 1 Relations And Functions · Exercise 1.1 Question 11

For points P,Q in a plane, define PRQ iff their distances from the origin are equal. Prove equivalence. For P≠(0,0), describe its class.

💡 Concept Hints

  1. Translate the relation into equality of distances before identifying the locus.
  2. Work through the definitions using the stated domain and codomain; justify a failed universal property with one valid counterexample.

✅ Step-by-Step Solution

Final Answer: The class of P is the circle centred at the origin of radius |OP|.
  1. Write PRQ as |OP|=|OQ|. Equality proves reflexivity and symmetry.
  2. If |OP|=|OQ| and |OQ|=|OR|, then |OP|=|OR|, proving transitivity.
  3. The class of P consists exactly of Q satisfying |OQ|=|OP|.
  4. Since P is not the origin, |OP|>0, and this locus is the stated circle, containing P.

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