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If the pair of straight lines represented by ax² + 2hxy + by² + 2gx + 2fy + c = 0 meet on the y-axis, then which relation must hold?

1. 2fgh = bg² + ch²
2. bg² = ch²
3. abc = 2fgh
4. none of these

Correct answer: 2fgh = bg² + ch²

Solution

The condition for the pair of straight lines to meet on the y-axis implies that the x-coefficient must vanish, leading to the relationship 2fgh = bg² + ch², which ensures that the lines intersect at a point where x equals zero.

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