The joint equation of the bisector of the angle between the lines 2 x^2+11 x y+3 y^2=0 is

Step-by-step solution

Given the equation of the pair of lines: 2x^2 + 11xy + 3y^2 = 0 . Compare with the general form ax^2 + 2hxy + by^2 = 0 , yielding a = 2 , 2h = 11 so h = 11 2 , and b = 3 . The joint equation of the bisectors is given by x^2 - y^2 a - b = xy h . Substituting the values: x^2 - y^2 2 - 3 = xy 11 2 Simplify to x^2 - y^2 -1 = 2xy 11 Cross-multiplying gives 11(x^2 - y^2) = -2xy , or 11x^2 - 11y^2 = -2xy Rearranged: 11x^2 + 2xy - 11y^2 = 0 This matches option A exactly.