The product of the perpendicular distances from the origin on the pair of straight lines 12 x^2+25 x y+12 y^2+10 x+11 y+2=0 , is

Step-by-step solution

Given that First we take homogeneous part of Eq. (i), aligned & i.e. 12 x^2+25 x y+12 y^2=0 & (3 x+4 y)(4 x+3 y)=0 aligned So, let the lines represented by Eq. (i) be The combined Eqs. of (ii) and (iii), we get gathered (3 x+4 y+c₁ ) (4 x+3 y+c₂ )=0 (3 x+4 y)(4 x+3 y)+c₁(4 x+3 y)+ c₂(3 x+4 y)+c₁ c₂=0 12 x^2+25 x y+12 y^2+ (4 c₁+3 c₂ ) x + (3 c₁+4 c₂ ) y+c₁ c₂=0 gathered On comparing the equation with Eq. (i), we get The perpendicular distance from origin to the equations (vi) and (vii) are aligned & p₁= |0+0+1| 3^2