If one of the lines represented by a x 2 + 2 h x y + b y 2 = 0 passes through ( 2 , 3 ) and the other passes through ( 4 , 5 ) , then a + 2 h + b equals

Step-by-step solution

Given that: a x 2 + 2 h x y + b y 2 = 0 Passing through ( 2 , 3 )   &   ( 4 , 5 ) Given equation passing through ( 0 , 0 ) As we know, Equation of line passing through two given points y - y 1 = y 2 - y 1 x 2 - x 1 ( x - x 1 ) Equation of the line through ( 0 , 0 )   &   ( 2 , 3 ) : y = 3 2 x ⇒ 3 x - 2 y = 0 Equation of the line through ( 0 , 0 )   &   ( 4 , 5 )   : y = 5 4 x ⇒ 5 x - 4 y = 0 Here, the pair of straight lines is ( 3 x - 2 y ) ( 5 x - 4 y ) =