Question

The line x - 2y = 0 is perpenrucular to one of the lines given by ax² + 2hxy + by² = 0, when ______.

Options

• a + 4b = 4h

• a + b = 4h

• 4a + b = h

• 4a + b = 4h

Answer 1

The line x - 2y = 0 is perpenrucular to one of the lines given by ax² + 2hxy + by² = 0, when a + 4b = 4h.

Explanation:

The auxiliary form of equation

ax² + 2hxy + by² = 0 is bm² + 2hm + a = 0

The slope of line x - 2y = 0 is `1/2`.

Since the given line is perpendicular to one of lines given by ax² + 2hxy + by² = 0, we have slope of one of the lines, m₁ = - 2

∴ Substituting in auxiliary equation, we get

b(- 2)² + 2h(- 2) + a = 0

⇒ 4b - 4h + a = 0

⇒ a + 4b = 4h