Question

Find the values of p and q, if the following equation represents a pair of perpendicular lines:
px² − 8xy + 3y² + 14x + 2y + q = 0.

Answer 1

Given equation is px² − 8xy + 3y² + 14x + 2y + q = 0

Comparing with

ax² + 2hxy + by² + 2gx + 2fy + c = 0, we get

a = p, h = − 4, b = 3, g = 7, f = 1, c = q.

The given equation represents a pair of lines perpendicular to each other

∴ a + b = 0

∴ p + 3 = 0

∴ p = −3

Also, the given equation represents a pair of lines

∴ −3(3q − 1) + 4( − 4q − 7) + 7(− 4 − 21) = 0

∴ −9q + 3 − 16q − 28 − 175 = 0

∴ −25q − 200 = 0

∴ −25q = 200

∴ q = −8 [1]x

∴ p = −3 and q = −8