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The pair of straight lines given by ax² + 2(a + b)xy + by² = 0 are diameters of a circle and split it into four sectors. If the area of one sector is three times the area of another sector, then which relation between a and b must hold?
- 3a² - 10ab + 3b² = 0
- 3a² - 2ab + 3b² = 0
- 3a² + 10ab + 3b² = 0
- 3a² + 2ab + 3b² = 0
Correct answer: 3a² + 2ab + 3b² = 0
Solution
The correct option indicates a specific relationship between the coefficients a and b that ensures the areas of the sectors created by the diameters of the circle are in the ratio of 3:1. This relationship arises from the geometric properties of the circle and the angles formed by the intersecting lines.
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