Find the Domain 1/49x^2+1/9y^2=1

Problem

1/49*x2+1/9*y2=1

Solution

1. Identify the type of equation. The equation is in the standard form of an ellipse centered at the origin, which is (x2)/(a2)+(y2)/(b2)=1

2. Determine the values of a2 and b2 In this equation, a2=49 and b2=9

3. Calculate the horizontal vertices. Since a2=49 we find a=√(,49)=7 The ellipse extends horizontally from x=−7 to x=7

4. Define the domain. The domain of a relation is the set of all possible xvalues. For this ellipse, x is restricted to the interval between the horizontal vertices.

5. Express the domain in interval notation. The values of x must satisfy −7≤x≤7

Final Answer

Domain:[−7,7]

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