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Question
Find the value of k if lines represented by kx2 + 4xy – 4y2 = 0 are perpendicular to each other.
Solution
Comparing the equation kx2 + 4xy – 4y2 = 0 with ax2 + 2hxy + by2 = 0, we get,
a = k, 2h = 4 and b = –4
Since lines represented by kx2 + 4xy – 4y2 = 0 are perpendicular to each other,
a + b = 0
∴ k – 4 = 0
∴ k = 4.
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