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If a line passes through the point P(1,-2) and cuts the circle `x^(2)+y^(2)-x-y=0` at A and B, then the maximum value of `PA+PB` is

A

`sqrt(a)`

B

8

C

`sqrt(8)`

D

`2sqrt(8)`

Text Solution

Verified by Experts

The correct Answer is:
A
We have, PA+ PAB = 2 PA+AB
Clearly, PA + PB is maximum when AB is maximum i.e. AB isa diameter of the circle.
Now,
PA+PB=(PC-AC)+(PC+CB)
`rArr PPB=2PC " " [:' AC=CB]`
`rArr PA+PB=2sqrt((1)/(4)+(25)/(4))=sqrt(26)`
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