Find the Domain 16x^2+9y^2=144

Problem

16*x2+9*y2=144

Solution

1. Identify the type of equation. This is the equation of an ellipse because both x2 and y2 terms are positive and have different coefficients.

2. Rewrite the equation in standard form by dividing both sides by 144

(16*x2)/144+(9*y2)/144=144/144

3. Simplify the fractions to find the lengths of the semi-axes.

(x2)/9+(y2)/16=1

4. Determine the horizontal boundaries. The standard form of an ellipse centered at the origin is (x2)/(a2)+(y2)/(b2)=1 Here, a2=9 which means a=3

5. Define the domain. For an ellipse centered at the origin, the xvalues are constrained between −a and a

−3≤x≤3

Final Answer

Domain: *[−3,3]

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