Question

The directrix of the parabola traced out by the centre of a moving circle which touches both the line y = -x and the circle (x - 3)² + (y - 4)² = 9 is

(A)   x + y - 3 = 0 

(B)   x + y + 3 = 0 

(C)   x + y - 3√2 = 0 

(D)   x - y- √2 = 0

Answer 1

Correct option (B)   x + y + 3 = 0 

Explanation :

See Fig. The directrix is the line parallel to x + y = 0 at a distance of 3 units from x + y = 0 to the left of x + y = 0. Therefore, the required line is x + y + 3 = 0.