JEE Main · 2021 · 27 Jul 2021 · Shift 1 · Circle

Let P and Q be two distinct points on a circle which has center at

C (2, 3)

and which passes through origin O . If OC is perpendicular to both the line segments CP and CQ , then the set

{P, Q}

is equal to :

(A) ${(- 1, 5), (5, 1)}$ ✓ Correct
(B) ${(2 + 22, 3 + 5), (2 - 22, 3 - 5)}$
(C) ${(2 + 22, 3 - 5), (2 - 22, 3 + 5)}$
(D) ${(4, 0), (0, 6)}$

Answer: (A)

Solution

The radius is

O C = 4 + 9 = 13

, and

C P

C Q

are radii perpendicular to

O C = (2, 3)

.
A vector perpendicular to

(2, 3)

with length

13

\pm (- 3, 2)

, so

P = (2, 3) + (- 3, 2) = (- 1, 5), Q = (2, 3) - (- 3, 2) = (5, 1)

The set of the two points is

{(- 1, 5), (5, 1)}

JEE Main · 2021 · 27 Jul 2021 · Shift 1 · Single correct option

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