Question

If ax² + 2xy – 3y² + 4x + c = 0 represents a pair of perpendicular lines, then ______.

Options

• a= 3, c =2

• a = 3, c = `6/5`

• a = 3, c = `4/5`

• a= 3, c = 6

Answer 1

If ax² + 2xy – 3y² + 4x + c = 0 represents a pair of perpendicular lines, then a = 3, c = `6/5`.

Explanation:

Comparing the given equation with

Ax² + 2Hxy + By² + 2Gx + 2Fy + C = 0, we get

A = a, B = –3, H = 1, G = 2, F = 0, C = c

Since the given lines are perpendicular,

A + B = 0

⇒ a – 3 = 0

⇒ a = 3

Since the given equation represents a pair of lines,

ABC+ 2FGH – AF² – BG² – CH² = 0

⇒ 3(–3)c + 3(2²) – c(1²) = 0

⇒ –10c + 12 = 0

⇒ c = `6/5`