JEE PYQ: Sets And Relations Question 4
Question 4 - 2021 (26 Feb Shift 1)
Let $R = {(P, Q) \mid P \text{ and } Q \text{ are at the same distance from the origin}}$ be a relation, then the equivalence class of $(1, -1)$ is the set:
(1) $S = {(x, y) \mid x^2 + y^2 = 1}$
(2) $S = {(x, y) \mid x^2 + y^2 = 4}$
(3) $S = {(x, y) \mid x^2 + y^2 = \sqrt{2}}$
(4) $S = {(x, y) \mid x^2 + y^2 = 2}$
Show Answer
Answer: (4)
Solution
$P(a, b), Q(c, d), PO = QO$
$\Rightarrow a^2 + b^2 = c^2 + d^2$
$R(x, y), \quad s = (1, -1) \Rightarrow RO = SO$
($\because$ equivalence class)
$x^2 + y^2 = 2$
BETA
