We have, S1:x2+y2+2x+8y−23=0 S2:x2+y2−4x+10y+19=0 Now, centres of both the circles are C1(−1,−4) and C2(2,−5) ∴ Pole of C1(−1,−4) with respect to S2 is
−x−4y−2(x−1)+5(y−4)+19=0 ⇒−x−4y−2x+2+5y−20+19=0
⇒−3x+y+1=0 ⇒3x−y−1=0....(i) and Pole of C2(2,−5) with respect to S1 is
2x−5y+(x+2)+4(y−5)−23=0 2x−5y+x+2+4y−20−23=0
3x−y−41=0.....(ii) Eqs. (i) and (ii) shows parallel lines and distance between them =|