# 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# .