Question: a) Find a first order differential equation satisfied by the circles in this family. Show all work justifying your answer. X ^ (2) + y

a) Find a first order differential equation satisfied by the circles in this family. Show all work justifying your answer.

X ^ (2) + y ^ (2) -2cy = a ^ (2) (circle family with centers on the y axis and that also pass through (a, 0), (-a, 0)


b) What is the differential equation satisfied by the orthogonal trajectories to the family of circles?


 

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