If a x^2+6 x y+b y^2-10 x+10 y-6=0 represents a pair of perpendicular lines, then the values of |a| equals

Step-by-step solution

Given pair of perpendicular lines are given as, a x^2+6 x y+b y^2-10 x+10 y-6=0 General equation is given as, a x^2+2 h x y+b y^2+2 g x+2 f y+c=0 Compare Eqs. (i) and (ii), we obtain aligned & a=a, 2 h=6 h=3, b=b, 2 g=-10 g=-5 & 2 f=10 f=5, c=-6 & | array lll a & h & g h & b & f g & f & c array |=0 | array ccc a & 3 & -5 3 & b & 5 -5 & 5 & -6 array |=0 & a(-6 b-25)-3(-18+25)-5(15-5 b)=0 & 25 a+25 b+6 a b+96=0 . aligned Since, lines are perpendicular a+b=0 or a=-b Use Eq. (iv) in Eq. (iii), array rlrl & 25(a-a)+6 a(