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Question
Show that 4x2 + 4xy + y2 − 6x − 3y − 4 = 0 represents a pair of parallel lines
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Solution
The equation of the given pair of straight lines is
4x2 + 4xy + y2 – 6x – 3y – 4 = 0 .......(1)
Compare this equation with the equation
ax2 + 2hxy + by2 + 2gx + 2fy + c = 0 .......(2)
a = 4
2h = 4
b = 1
2g = – 6
2f = – 3
c = – 4
The condition for parallelism is
h2 – ab = 0
22 – (4)(1) = 4 – 4 = 0
∴ The given pair of straight lines represents a pair of parallel straight lines.
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