=1‌‌‌⋅⋅⋅⋅⋅⋅⋅(i) where,a=√5,b=2 As we know that, equation of any tangent to the hyperbola Eq. (i) having slopemis y=mx±√a2m2−b2=mx+√5m2−4‌‌‌⋅⋅⋅⋅⋅⋅⋅(ii) According to question, Eq. (ii) passes through(1,1). So,1=m×1±√5m2−4 ‌⇒‌‌1−m=±√5m2−4 ‌⇒‌‌(1−m)2=5m2−4 ‌⇒‌‌4m2+2m−5=0‌‌‌⋅⋅⋅⋅⋅⋅⋅(iii) Letm1,m2slopes of these two tangents be the roots of Eq. (iii). So,m1+m2=‌