Question

The centre of the circle passing through (0, 0) and (1, 0) and touching the circle x² + y² = 9 is ……..

(a) [(3/2), (1/2)]

(b) [(1/2), (3/2)]

(c) [(1/2), (1/2)]

(d) [(1/2), ±√2]   

Answer 1

The correct option (d) [(1/2), ±√2]   

Explanation:

Let circle be x² + y² +2gx + 2fy + c = 0

This passes through (0, 0) and (1, 0).

∴ c = 0 and 1 + 2g = 0 ⇒ g = – (1/2).

also this circle touches x² + y² = g. 

The centre of this circle (0, 0) lies on the above circle.

⇒ Circle touches internally the circle x² + y² = 9.

∴ Diameter of required circle must be equal to radius of the circle

 x² + y² = 9. 

∴   2√(g² + f²) = 3

∴     2√[(1/4) + f²] = 3

∴      (1/4) + f² = (9/4) 

∴   f = ± √2

∴ Centre of required circle is [(1/2), ±√2].