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If P(2, 8) lies inside the circle x² + y² - 2x + 4y - p = 0 and the circle neither touches nor intersects the coordinate axes, find the set of values of p.
- p < -1
- p < -4
- p > 96
- empty set (phi)
Correct answer: empty set (phi)
Solution
The interior condition forces p to be large (p > 96 roughly), while the conditions that the circle avoids both axes force p to be small/negative; these requirements are mutually exclusive, so no p satisfies all of them and the set is empty.
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