Question

The pair of lines represented by 3ax² + 5xy + (a² – 2)y² = 0 are perpendicular to each other for ______.

Options

• two values of a

• ∀ a

• for one value of a

• for no values of a

Answer 1

The pair of lines represented by 3ax² + 5xy + (a² – 2)y² = 0 are perpendicular to each other for two values of a.

Explanation:

We know that pair of straight lines

ax² + 2hxy + by² = 0 are perpendicular when a + b = 0

3a + a² – 2 = 0

⇒ a² + 3a – 2 = 0; 

⇒ a = `(-3 ± sqrt(9 + 8))/2` = `(-3 ± sqrt(17))/2`