Well, i'm getting slightly different answer, so i'm posting my method, plz do correct me in case i'm wrong.
Intersection points would be P(0,c1) , Q(0,c2) R(c2-c1/m1-m2 , m1c2-m2c1/m1-m2)
Now, using determinant, i'm getting the area as
1/2* [c12 +c22-2c1c2]/m1-m2
=(c1-c2)2/2(m1-m2)
Hence, if c1=c2, therefore area=0
Plz do tell me if i'm wrong.
Thank you.