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The second-degree equation 6x² - alpha*x*y - 3y² - 24x + 3y + beta = 0 represents a pair of straight lines whose point of intersection lies on the x-axis. Find the value of 20*alpha - beta.
- 1
- 2
- 6
- 4
Correct answer: 6
Solution
Setting the partial derivatives to zero with y = 0 gives x = 2 and alpha = 3/2. Substituting the vertex (2, 0) into the original equation gives beta = 24. Hence 20*alpha - beta = 30 - 24 = 6.
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