If the pair of lines `ax^2+2hxy+by^2= 0 (h^2 > ab)` forms an equilateral triangle with the line `lx + my + n=0` then `(a+3b)(3a+b)=`

If the pair of lines ax^(2)+2hxy+by^(2)=0 (h^(2) gt ab) orms an equilateral triangle with the line lr + my + n = 0 then (a+3b)(3a+b)=

If the pair of lines given by a x^(2)+2 h x y+b y^(2)=0 (h^(2)>a b) forms an equilateral triangle with A x+B y+C=0 then (a+3 b)(3 a+b)=

Prove that the line lx+my+n=0 and the pair of lines (lx+my)^2-3(mx-ly)^2=0 form an equilateral triangle and its area is (n^2)/(sqrt(3)(l^2+m^2))

The line lx+my+n=0 touches y^(2)=4ax

If the pairs of lines ax^2+2hxy+by^2=0 and a'x^2+2h'xy+b'y^2=0 have one line in common, then (ab'-a'b)^2 is equal to

If the acute angle between the lines ax^2+2hxy +by^2=0 is 60^@ then show that (a+3b)(3a+b)= 4h^2

If one of the pair of lines ax^2+2hxy+by^2=0 bisects the angle between positive directions of the axes, a, b, h satisfy the relation

Statement 1: If -2h =a+b , then one line of the pair of lines ax^(2)+2hxy+by^(2)=0 bisects the angle between coordinate axes in positive quadrant. Statement 2: If ax + y (2h + a) = 0 is a factor of ax^(2)+2hxy+by^(2)=0 , then b + 2h +a=0

The pair of lines a^(2)x^(2)+2h(a+b)xy+b^(2)y^(2)=0 and ax^(2)+2hxy+by^(2)=0 are