The two pairs of straight lines 12 x^2+7 x y-12 y^2=0 and 12 x^2+7 x y-12 y^2-x+7 y-1=0 constitute a

Step-by-step solution

aligned & 12 x^2+7 x y-12 y^2=0 & 12 x^2+16 x y-9 x y-12 y^2=0 & 4 x(3 x+4 y)-3 y(3 x+4 y)=0 & (4 x-3 y)(3 x+4 y)=0 & 4 x-3 y=0 and 3 x+4 y=0 aligned Slope of the two lines are 4 3 and -3 4 , respectively. The two lines are perpendicular. aligned & 12 x^2+7 x y-12 y^2-x+7 y-1=0 & 12 x^2+x(7 y-1)-12 y^2+7 y-1=0 & x=- b+ b^2-4 a c 2 a & x=- (7 y-1) (7 y-1)^2-4 12 (-12 y^2+7 y-1 ) 2 12 & x= 1-7 y 49 y^2+1-14 y-336 y+48+576 y^2 24 & 24 x=1-7 y 625 y^2-350 y+49 & 24 x=1-7 y (25 y-7) & 24 x=1-7 y+25 y-7 or 24 x=1-7 y-25