Multivariable Calculus

How to solve

The equation f(x, y) = c for f = x² + y² is the circle of radius √c centered at the origin. Once you have the radius, the usual circle formulas apply.

Steps

  1. If you know c, radius is √c.
  2. If you see radius r, then c = r².
  3. Diameter is 2r; circumference is 2πr; area is πr².

Example

x² + y² = 9

  1. r = √9 = 3.
  2. Level value c = r² = 9.
  3. Diameter = 2r = 6; circumference = 2πr = 6pi; area = πr² = 9pi.

Answer: depends on the prompt — 3 (radius), 9 (level c), 6 (diameter), 6pi (circumference), or 9pi (area)

How to type answers

  • Multiples of pi like 16pi
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