If the pairs of straight lines represented by 3 x^2+2 h x y-3 y^2=0 and 3 x^2+2 h x y-3 y^2+2 x-4 y+c=0 form a square, then (h, c)=

Step-by-step solution

Given, equations of pair of straight lines both represents pair of perpendicular lines. Now, the point of intersection the lines given by a x^2+2 h x y+b y^2+2 g x+2 f y+c=0 is ( h f-b g a b-h^2 , g h-a f a b-h^2 ) , So for the pair of lines (ii), the point of intersection is aligned & A ( h(-2)-(-3)(1) -9-h^2 , h-3(-2) -9-h^2 ) & =A ( 2 h-3 9+h^2 ,- h+6 9+h^2 ) aligned The equation of diagonal of square passes through and the equation of diagonal of square not passes The diagonals given by the Eqs. (iii) and (iv)