Equation of circle ⇒(x+10)2+y2=4 Equation of tangent to circle x2+y2=a2 is y=mx±a√1+m2 Here, equation of tangent y=m(x+10)±2√1+m2 ⇒y=mx+10m±2√1+m2 On comparing this equation with y=mx+c , we get c=10m±2√1+m2⋅⋅⋅⋅⋅⋅⋅(i) This equation is also a focal chord of y2=−64x whose focus is at (−16,0) . So, it must pass through (−16,0). y=mx+c ⇒0=−16m+c ∴c=16m⋅⋅⋅⋅⋅⋅⋅(ii) From Eqs. (i) and (ii), 16m=10m±2√1+m2 ⇒6m=±2√1+m2 ⇒9m2=1+m2 ⇒m=