Area of the region enclosed by the curves 3 x^2-y^2-2 x y+4 x+1=0 and 3 x^2-y^2-2 x y+6 x+2 y=0 is

Step-by-step solution

Given equation of curve is aligned & 3 x^2+(4-2 y) x+1-y^2=0 & x= (2 y-4) (4-2 y)^2-4 3 (1-y^2 ) 6 & - 2(y-2) 4(2 y-1)^2 6 = (y-2) (2 y-1) 3 aligned Equation of pair of lines are aligned & L₁: x-y+1=0 ...(i) & L₂: 3 x+y+1=0...(ii) aligned On solving (i) ằnd (ii), we get x= -1 2 and y= 1 2 Another equation of curve is aligned & 3 x^2+(6-2 y) x+2 y-y^2=0 & x= (2 y-6) (6-2 y)^2-4 3 (2 y-y^2 ) 6 & = (2 y-6) 2(2 y-3) 6 = (y-3) (2 y-3) 3 aligned Equation of pair of lines are aligned & L₃: x-y+2=0...(iii) & L₄: 3 x+y=0...