JEE Main 2017 — Circle Question with Solution
From: JEE Main 2017 (Online) 8th April Morning Slot
Question
If a point P has co-ordinates (0, 2) and Q is any point on the circle, x2 + y2 5x y + 5 = 0, then the maximum value of (PQ)2 is :
Choose an option
Show full solutionCorrect option: B
Correct answer
B14 +
Step-by-step explanation
Given that x2 + y2 5x y + 5 = 0
(x 5/2)2 + (y 1/2)2 1/4 = 0
(x 5/2)2 + (y 1/2)2 = 3/2
on circle [ Q (5/2 + cos Q, + sin Q)]
PQ2 = +
PQ2 = (cos Q + sinQ)
= 14 + 5 (cosQ + sinQ)
Maximum value of PQ2
= 14 + 5 = 14 + 5
(x 5/2)2 + (y 1/2)2 1/4 = 0
(x 5/2)2 + (y 1/2)2 = 3/2
on circle [ Q (5/2 + cos Q, + sin Q)]
PQ2 = +
PQ2 = (cos Q + sinQ)
= 14 + 5 (cosQ + sinQ)
Maximum value of PQ2
= 14 + 5 = 14 + 5
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This is a previous-year question from JEE Main 2017, covering the Circle chapter of Mathematics. PrepSharp catalogues every PYQ from JEE Main with a verified answer key and step-by-step solution prepared by IIT alumni — so you can search by chapter, topic or year and revise efficiently.