AP EAPCET 20-Aug-2021 Shift 2 Paper

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=5Then, 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