The correct option is
B x2+y2−2y=cGiven equations of the family of straight lines is y=mx+1
Here m is the arbitrary constant or parameter.
Now,differentiating the equation with respect to x gives.,
dydx=m
Substituting the value of m in the equation gives.,
y=x˙y+1
Now,to find the equation of the orthogonal trajectory wwe need to replace dydx by −dxdy which gives.,
(y−1)dy=−xdx
Integrating both sides of the equation gives.,
y22−y=−x22+c
Rearranging the terms gives.,
x2+y2−2y=c, where c is a constant.