If the common chord of the circles `x^(2) + ( y -lambda)^(2) =16` and `x^(2) +y^(2) =16` subtend a right angle at the origin then `' lambda'` is equal to `:`

Options

A. 4
B. `4sqrt(2)`
C. `pm 4 sqrt(2)`
D. 8

Answer

C

Explanation

The equation of the common chord is
`-2by+b^(2)=0 rArr y -(b)/(2)=0`
The combined equation fo the straight lines joining the origin to the points of intersection of y=b/2 and `b^(2)+ y^(2)-16` is
`x^(2)+y^(2)=16((2y)/(b))^(2)rArr b^(2) x^(2)+(b^(2)-64)y^(2)=0`
This equation represents a pair of perpendicular lines.
`:. b^(2)+b^(2)-64=0 rArr b = pm 4 sqrt(2)`