If one of the lines given by the equation 2 x^2+a x y+3 y^2=0 coincide with one of those given by the equation 2 x^2+b x y-3 y^2=0 , while the other two lines are perpendicular to each other, then the values of a and b are

Step-by-step solution

Given, equation of pair of straight line 2 x^2+a x y+3 y^2=0 and 2 x^2+b x y-3 y^2=0 Let the slope of line m and m₁ of the equation 2 x^2+a x y+3 y^2=0 m+m₁= -a 3 and m m₁= 2 3 Slope of the other line is m and m₂ . Then, m+m₂= b 3 and m m₂=-2 / 3 Given, m₁ m₂=-1 ...(i) m m₁ m m₂ =-1 m₁=-m₂ m₁+m₂=0 ...(ii) From Eqs. (i) and (ii), we get m₁=1 and m₂=-1 m=2 / 3m+m₁=-a / 3 2 3 +1=-a / 3 a=-5 and m+m₂=b / 3 2 3 -1=b / 3 b=-1 a=-5 and b=-1