Equation parallel to X -axis is given as y=a⇒y−a=0 ...(i) If Eq. (i) touches the circle x2+y2−6x−4y−12=0 ...(ii) Then, Eq. (i) becomes tangent to circle. Centre of Eq. (ii) is (3,2) Radius of Eq. (ii) is √9+4+12=5
Then, perpendicular distance from centre to line (i) is radius i.e. Perpendicular distance between (3,2) and y−a=0 is equal to 5 i.e.|
2−a
1
|=5 ⇒2−a=±5⇒a=7,−3 ∴ Equation of pair of lines =(y+3)(y−7)=0 i.e. (y+3)(y−7)=0 ⇒y2−4y−21=0