Let a and b be non-zero real such that a b . Then, the equation of the line passing through the origin and the point of intersection of x a + y b =1 and x b + y a =1 is

Step-by-step solution

Given, equation of lines are aligned & x a + y b &=1 & (i) and & x b + y a &=1 & (ii) & b x+a y &=a b & (iii) and & a x+b y &=a b & (iv) aligned Solving Eqs. (iii) and (iv), we get (a²-b² ) y=a² b-a b²=a b(a-b) y= a b a+b Substituting the value of y in Eq. (iii), we get aligned & b x+a ( a b a+b )=a b b x=a b- a² b a+b & b x= a b² a+b x= a b a+b aligned Point of intersection is ( a b a+b , a b a+b ) . Since, equation of the line passing through origin is y=m x When it passes through ( a b a+b , a b a+b ) , then we