Suppose the pairs of straight lines 2 x^2+a x y+3 y^2=0 and 2 x^2+b x y-3 y^2=0 are such that they have one common line with the other two remaining perpendicular. Then the values of a and b respectively are

Step-by-step solution

For a x^2+2 h x y+b y^2=0 ...(i) If the slope of 2 lines representing ...(i) are m₁ and m₂ then aligned & m₁+m₂=-2 h / b & m₁ m₂=a / b aligned For 2 x^2+a x y+3 y^2=0 ...(ii) If slope of common line is m and slope of other 2 are m₁ and m₂ respectively aligned & m+m₁=-a / 3, m . m₁=2 / 3 & m+m₂= b / 3, m m₂=-2 / 3 & m m₁=-m m₂ & m₁=-m₂ aligned other 2 lines are perpendicular aligned & m₁ m₂=-1 & m₂=-1 / m₁ & m₁=-m₂=- ( -1 m₁ ) & m₁^2=1 & m₁= 1 & m₂= 1 aligned For m₁=1 and m₂=-1 aligned & m=2 / 3 & m+m₁=- a 3 = 2 3 +