Question: Find the value of p, if the lines represented by the following equations coincide to each other: 2x² +pxy +2y² = 0.
Solution:
Given,
Equation of line is $2x² +pxy +2y² = 0$
or, 2x² +2×\frac{p}{2}xy + 2y² = 0 - (i)
Comparing equation (i) with ax² + 2hxy + by²=0, we get,
a = 2, h = \frac{p}{2}, and b = 2
We know, when two lines are coincident, h² = ab,
or, h² = ab
or, 2² = \frac{p}{2} × 2
or, 4 = p
\therefore p = 4
Therefore, the required value of p, when the lines represented by the given equation coincide to each other is 4.
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