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A rectangle of maximum area is inscribed...

A rectangle of maximum area is inscribed in the circle `|z-3-4i|=1.` If one vertex of the rectangle is `4+4i ,` then another adjacent vertex of this rectangle can be a. `2+4i` b. `3+5i` c. `3+3i` d. `3-3i`

A

`2+ 4i`

B

`3+5i`

C

`3+3i`

D

`3-3i`

Text Solution

Verified by Experts

The correct Answer is:
B, C

Clearly ,the inscribed rectangle is a square. Let the adjacement vertex be. Then
`(3+4i -(z))/((3+ 4i)-(4+ 4i)) =e^(pmipi//2)` (by rotation about centre)
`rArr 3+ 4i-z = pm i(-1)`
`rArr z =3 + 4 i pm = 3 + 5i or 3+ 3i`
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