The possible number of values of a for which the common chord of the circles x 2 + y 2 = 8 and x - a 2 + y 2 = 8 subtends a right angle at the origin is

Step-by-step solution

Equation of the common chord is x - a 2 + y 2 - 8 - x 2 - y 2 + 8 = 0 ⇒ - 2 a x + a 2 = 0 ⇒ x = a 2 If the chord x = a 2 subtends a right angle at 0,0 then the distance of x = a 2 from the origin is equal to 2 2 cos ⁡ 45 o = 2 ⇒ a = 4 or - 4