Find the Domain -16x^2+9y^2-144=0

Problem

−16*x2+9*y2−144=0

Solution

1. Identify the type of equation by rearranging it into standard form.

2. Add 144 to both sides of the equation.

−16*x2+9*y2=144

3. Divide every term by 144 to set the right side to 1

(−16*x2)/144+(9*y2)/144=144/144

4. Simplify the fractions to reveal the standard form of a hyperbola.

(y2)/16−(x2)/9=1

5. Determine the domain by analyzing the constraints on x In the equation of a hyperbola opening vertically (along the y-axis) in the form (y2)/(a2)−(x2)/(b2)=1 the variable x can take any real value because there are no square roots or denominators containing x that could be zero or undefined for specific real numbers.

6. Conclude that the domain is the set of all real numbers.

Final Answer

Domain: *(−∞,∞)

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