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The equation x²/(29 - p) - y²/(4 - p) = 1 (with p not equal to 4 or 29) represents which of the following?

1. An ellipse if p lies between 4 and 29
2. A hyperbola if p lies between 4 and 29
3. An ellipse if p is greater than 29
4. No real curve if p is less than 4

Correct answer: An ellipse if p lies between 4 and 29

Solution

For 4 < p < 29, (29 - p) > 0 and (4 - p) < 0, so the equation becomes x²/(positive) + y²/(positive) = 1, an ellipse.

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