The given equation represents a pair of lines perpendicular to each other
∴ (coefficient of x2) + (coefficient of y2) = 0
∴ p + 3 = 0 p = -3
With this value of p, the given equation is
– 3x2 – 8xy + 3y2 + 14x + 2y + q = 0.
Comparing this equation with
ax2 + 2hxy + by2 + 2gx + 2fy + c = 0, we have,
a = -3, h = -4, b = 3, g = 7, f = 1 and c = q.
= -3(3q – 1) + 4(-4q – 7) + 7(-4 – 21)
= -9q + 3 – 16q – 28 – 175
= -25q – 200= -25(q + 8)
Since the given equation represents a pair of lines, D = 0
∴ -25(q + 8) = 0 ∴ q= -8.
Hence, p = -3 and q = -8.