Question #d6ef5
1 Answer
Feb 11, 2017
The differential equation for the family of circles is:
#dy/dx = (r+x)/(r-y)# where#r>0# .
Explanation:
The general equation of a circle with centre
# (x-a)^2 + (y-b)^2 = r^2 #
If we want the circle in the second quadrant then we require the centre
# (x+r)^2 + (y-r)^2 = r^2 \ \ \ \ \ \ \ # where#r>0#
Differentiating wrt
# 2(x+r) + 2(y-r)dy/dx = 0 #
# :. (x+r) + (y-r)dy/dx = 0 #
# :. (y-r)dy/dx = -(x+r) #
# :. dy/dx = (r+x)/(r-y) #
So the differential equation for the family of circles is:
#dy/dx = (r+x)/(r-y)# where#r>0# .
