The circle x2+y2−8x=0 and hyperbola x29−y24=1 intersect at the points A and B.
Equation of a common tangent with positive slope to the circle as well as to the hyperbola is
2x−√5y+4=0
Equation of tangent to hyperbola having slope m is
y=mx+√9m2−4 ...(i)
Equation of tangent to circle is
y=m(x−4)+√16m2+16 ...(ii)
Eqs. (i) and (ii) will be identical for m=2√5 satisfy.
∴ Equation of common tangent is 2x−√5y+4=0.