← 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
- If you know c, radius is √c.
- If you see radius r, then c = r².
- Diameter is 2r; circumference is 2πr; area is πr².
Example
x² + y² = 9
- r = √9 = 3.
- Level value c = r² = 9.
- 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
Loading drills…