Form the differential equation of the family of circles in the first quadrant which touch the coordinate axes.

Question

$(A)\;(x−y )^2 (1- y ′ )^2 =(x+y y ′ )^2$
$(B)\;(x−y )^2 (1+ y ′ )^2 =(x-y y ′ )^2$
$(C)\;(x−y )^2 (1+ y ′ )^2 =(x+y y ′ )^2$
$(D)\;(x+y )^2 (1+ y ′ )^2 =(x+y y ′ )^2$