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A(1/(sqrt(2)),1/(sqrt(2))) is a point on...

`A(1/(sqrt(2)),1/(sqrt(2)))` is a point on the circle `x^2+y^2=1` and `B` is another point on the circle such that arc length `A B=pi/2` units. Then, the coordinates of `B` can be (a) `(1/(sqrt(2)),-1/sqrt(2))` (b) `(-1/(sqrt(2)),1/sqrt(2))` (c) `(-1/(sqrt(2)),-1/(sqrt(2)))` (d) none of these

A

`(-1,2sqrt(2))`

B

`(2sqrt(2),1)`

C

`((23)/(9),(10sqrt(2))/(9))`

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
B

`(x_(1)-1)/(cos theta) =(y_(1)-2sqrt(2))/(sin theta) =2` (using parametric form of straight line)
Also, `x_(1)^(2) +y_(1)^(2) =9`
On solving, we get
`(1+2 cos theta)^(2) +(2sqrt(2)+2 sin theta)^(2) =9`
`cos theta =(7)/(9)` or `-1`
Then the required point is `(-1,2sqrt(2)), ((23)/(9),(10sqrt(2))/(9))`
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