QJEEAdv08Mafd54: JEE Advanced 2008 Mathematics - Class 11 JEEAdv08Mafd54 Solution: Let z be any point A ∩ B ∩ C and let w be any point satisfying…

Question

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Let z be any point $A \cap B \cap C$ and let w be any point satisfying $| w - 2 - i | < 3$ . Then, $| z | - | w | + 3$ lies between :

Accepted Answer

Since, $| w - (2 + i) | < 3$

$| w | - | 2 + i | < 3$

$- 3 + \sqrt{5} < | w | < 3 + \sqrt{5}$

$- 3 - \sqrt{5} < | w | < 3 - \sqrt{5}$

Also, $| z - (2 + i) | = 3$

$- 3 + \sqrt{5} \leq | z | \leq 3 + \sqrt{5}$

$∴$ $- 3 < | z | - | w | + 3 < 9$

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