What is the differential equation representing the family of concentric circles centered at the origin, , where is an arbitrary parameter?

Answer and explanation

Correct answer: D.

  1. Step 1: Start with the family equation: .
  2. Step 2: Differentiate implicitly with respect to : .
  3. Step 3: Divide the entire equation by : .
Answer
.
Why not the others: is the differential equation for straight lines passing through the origin (); corresponds to hyperbolas ; changes the sign on the derivative term.

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