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Find the combined equation of the two straight lines passing through the point (1, 0) and parallel to the pair of lines given by 2x² - xy - y² = 0.

1. 2x² - xy - y² - 4x - y = 0
2. 2x² - xy - y² - 4x + y + 2 = 0
3. 2x² + xy + y² - 2x + y = 0
4. None of these

Correct answer: 2x² - xy - y² - 4x + y + 2 = 0

Solution

The correct option represents the combined equation of two lines that are parallel to the original pair of lines defined by the quadratic equation and also pass through the specified point (1, 0). By substituting the point into the equation, it confirms that the lines intersect at that point, thus validating the solution.

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