To make the given curves x2+y2=4 and x+y=a homogeneous. ∴‌x2+y2−4(‌
x+y
a
)2=0 ⇒a2(x2+y2)−4(x2+y2+2xy)=0 ⇒x2(a2−4)+y2(a2−4)−8xy=0 Since, this is a perpendicular pair of straight lines. ∴‌a2−4+a2−4=0 ⇒a2=4⇒a=±2 Hence, required set of a is {−2,2}.
