Given, equation (a2−3)x2+16xy−2ay2+4x−8y−2=0 represents a pair of perpendicular line ‌∴(a2−3)+(−2a)=0 ‌⇒‌‌a2−2a−3=0 ‌⇒‌‌a2−3a+a−3=0 ‌⇒‌‌a(a−3)+1(a−3)=0 ‌⇒‌‌(a−3)(a+1)=0 ‌⇒‌‌a=3,−1 ⇒a=3, since for a=−1 lines does not exists.