Find the Domain 9x^2-4y^2=36

Problem

9*x2−4*y2=36

Solution

1. Identify the type of equation. This is the equation of a hyperbola because it follows the form A*x2−B*y2=C where A and B are positive.

2. Rewrite the equation in standard form by dividing both sides by 36

(9*x2)/36−(4*y2)/36=36/36

3. Simplify the fractions to reveal the standard form of a horizontal hyperbola.

(x2)/4−(y2)/9=1

4. Solve for y to determine the restrictions on x

(y2)/9=(x2)/4−1

y2=9*((x2)/4−1)

y=±3√(,(x2)/4−1)

5. Set the radicand to be greater than or equal to zero, as the square root of a negative number is not a real number.

(x2)/4−1≥0

(x2)/4≥1

x2≥4

6. Determine the intervals for x by taking the square root of both sides.

|x|≥2

x≤−2* or *x≥2

Final Answer

Domain: *(−∞,−2]∪[2,∞)

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