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

Problem

16*x^2+9*y^2=144

Solution

1. Identify the type of equation. This is the equation of an ellipse because both x^2 and y^2 terms are positive and have different coefficients.

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

(16*x^2)/144+(9*y^2)/144=144/144

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

(x^2)/9+(y^2)/16=1

4. Determine the horizontal boundaries. The standard form of an ellipse centered at the origin is (x^2)/(a^2)+(y^2)/(b^2)=1 Here, a^2=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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