If the area of the triangle formed by the lines y=x+c and 2 x^2+5 x y+3 y^2=0 is 1 20 sq. units, then c=

Step-by-step solution

aligned & 2 x^2+5 x y+3 y^2=0 & (x+y)(2 x+3 y)=0 aligned Let ABC be the region formed by aligned & Now, area of ABC = | array lll x₁ & y₁ & 1 x₂ & y₂ & 1 x₃ & y₃ & 1 array |= | array ccc 0 & 0 & 1 - c 2 & c 2 & 1 - 3 c 5 & 2 c 5 & 1 array | & 1 20 =0+0+1 [ (- c 2 ) ( 2 c 5 )- ( c 2 ) (- 3 c 5 ) ] & c^2=1 c= 1 aligned