Find the Domain x^2+y^2=13

Problem

x2+y2=13

Solution

1. Identify the equation as a circle centered at the origin (0,0) with a radius squared r2=13

2. Solve for y in terms of x to determine the set of possible xvalues.

y2=13−x2

y=±√(,13−x2)

3. Set the radicand to be greater than or equal to zero, as the square root of a negative number is not defined in the set of real numbers.

13−x2≥0

4. Solve the inequality for x

x2≤13

−√(,13)≤x≤√(,13)

5. Express the domain in interval notation.

Final Answer

Domain:[−√(,13),√(,13)]

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