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Question
Find the value of h, if the measure of the angle between the lines 3x2 + 2hxy + 2y2 = 0 is 45°.
Solution
Given equation of the lines is 3x2 + 2hxy + 2y2 = 0
Comparing with ax2 + 2hxy + by2 = 0,
We get a = 3, b = 2
Given that 45° is the acute angle between the lines.
∴ tan (45°) = `|(2sqrt("h"^2 - "ab"))/("a" + "b")|`
∴ 1 = `|(2sqrt("h"^2 - (3)(2)))/(3 + 2)|`
∴ 1 = `|(2sqrt("h"^2 - 6))/5|`
∴ `(5/2)^2` = h2 – 6
∴ h2 = `25/4 + 6`
∴ h2 = `49/4`
∴ h = `± 7/2`
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