Question

The length of the common chord of the ellipse (x-1)^2/9 + (y-2)^2/4 = 1 and the circle (x-1)^2 + (y-2)^2 = 1 is

a)2
b)sqrt(3)
c)4
d)none of these

Answer 1

D is the answer. \[\frac{ (x-1)^{2} }{ 3^{2} } + \frac{ (y-2)^{2} }{ 2^{2} } = 1 \rightarrow 2a = 6, 2b = 4.\]
\[(x-1)^{2} + (y-2)^{2} = 1 \rightarrow R = 1. \]
The ellipse and the circle can never intersect due to the above conditions and also because they are concentric.

Answer 2

the co-ordinate axes can be translated to the point (1,2), the length of the commoon chord doesn't change.