The given equation is
2x2 + 8xy + py2 + qx + 2y – 15 = 0
Comparing it with ax2 + 2hxy + by2 + 2gx + 2fy + c = 0, we get,
a = 2, h = 4, b = p, g = q/2, f = 1, c = – 15
Since the lines are parallel, h2 = ab
∴ (4)2 = 2p
∴ P = 8
Since the given equation represents a pair of lines
i.e. – 242 + 240 + 2q + 2q – 2q2 = 0
i.e. -2q2 + 4q – 2 = 0
i.e. q2 – 2q + 1 = 0
i.e. (q – 1)2 = 0
∴ q – 1 = 0
∴ q = 1.
Hence, p = 8 and q = 1.
