A pair of perpendicular straight lines passes through the origin and also through the point of intersection of the curve x^2+y^2=4 with x+y=a . The set containing the value of ' a ' is

Step-by-step solution

To make the given curves x^2+y^2=4 and x+y=a homogeneous. array rlrl & & x^2+y^2-4 ( x+y a )^2 & =0 & & a^2 (x^2+y^2 )-4 (x^2+y^2+2 x y ) & =0 & x^2 (a^2-4 )+y^2 (a^2-4 )-8 x y & =0 array Since, this is a perpendicular pair of straight lines. array ll & a^2-4+a^2-4=0 & a^2=4 a= 2 array Hence, required set of a is -2,2 .