Find the Domain x^2+y^2=68

Problem

x2+y2=68

Solution

1. Identify the equation as a circle centered at the origin (0,0) with the general form x2+y2=r2

2. Determine the radius squared by comparing the equations, which gives r2=68

3. Calculate the radius r by taking the square root of both sides, resulting in r=√(,68)=2√(,17)

4. Solve for y to express the relation as a function of x yielding y=±√(,68−x2)

5. Set the radicand to be greater than or equal to zero to ensure real values, resulting in 68−x2≥0

6. Find the interval for x by solving the inequality x2≤68 which leads to −√(,68)≤x≤√(,68)

Final Answer

Domain: *[−√(,68),√(,68)]

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