If the equation 8 x^2+8 x y+2 y^2+26 x+13 y+15=0 represents a pair of parallel straight lines, then the distance between them is.........

Step-by-step solution

Given equation is 8 x^2+8 x y+2 y^2+26 x+13 y+15=0 ...(i) On writing Eq. (i) as quadratic equation in x , we get 8 x^2+2 x(4 y+13)+2 y^2+13 y+15=0x= -2(4 y+13) 4(4 y+13)^2-32 (2 y^2+13 y+15 . 16 x= -(4 y+13) 7 8 aligned & 8 x=-4 y-13+7 or 8 x=-4 y-13-7 & 4 x+2 y+3=0 or 2 x+y+5=0 & 2 x+y+3 / 2=0 or 2 x+y+5=0 aligned d= | c₁-c₂ a^2+b^2 | , where, c₁=5, c₂=3 / 2, a=2, b=1d= | 5-3 / 2 2^2+1^2 |= 7 2 5