The center(s) of the circle(s) passing through the points (0, 0) and (1, 0) and touching the circle `x^2+y^2=9` is (are)

Options

A. `(3//2,1//2)`
B. `(1//2,3//2)`
C. `(1//2,2^(1//2))`
D. `(1//2,-2^(1//2))`

Answer

3,4

Explanation

From the diagram,
`sqrt(((1)/(2))^(2)+lambda^(2))=(3)/(2)` or `lambda = +- sqrt(2)`
Hence, the centres of the circle are `(1//2, +- sqrt(2))`