`(1, 2sqrt2)`is a point on circle, `x^2 + y^2 = 9`. Which of the following is not the point on the circle at 2 units distance from `(1, 2sqrt2)`?

Options

A. `(-1,2sqrt(2))`
B. `(2sqrt(2),1)`
C. `((23)/(9),(10sqrt(2))/(9))`
D. None of these

Answer

B

Explanation

`(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))`