The equation of the pair of lines joining the origin to the points of intersection of two circles x^2+y^2-4 x+8 y+5=0 and x^2+y^2+2 x+4 y-3=0 is

Step-by-step solution

Then, equation of common chord in given by aligned & S₁-S₂ & =0 & (x^2+y^2-4 x+8 y+5 ) & & & & - (x^2+y^2+2 x+4 y-3 ) & =0 & -6 x+4 y+8 & =0 & -3 x+2 y+4 & =0 & 3 x-2 y & =4 aligned Now, the required equation of pair of lines is given by homogenization of Eqs. (i) and (iii) or Eqs. (ii) and (iii) On homogenization of Eqs. (i) and (iii), we get aligned x^2+y^2-4 x ( x 4 / 3 + y -2 )+8 y ( x 4 / 3 . & .+ y -2 ) +5 ( x 4 / 3 + y -2 )^2 & =0 aligned aligned & x^2+y^2-4 x ( 3 4 x- y 2 )+8 y ( 3 4 x+ y -2 ) & +5 ( 3 x 4