Question

Find a if the sum of the slopes of lines represented by ax² + 8xy + 5y² = 0 is twice their product.

Answer 1

Comparing the equation ax² + 8xy + 5y² = 0 with ax² + 2hxy + by² = 0,

we get, a = a, 2h = 8, b = 5

Let m₁ and m₂ be the slopes of the lines represented by ax² + 8xy + 5y² = 0.

∴ m₁ + m₂ = `(- 2"h")/"b" = -8/5`

and m₁m₂ = `"a"/"b" = "a"/5`

Now, (m₁ + m₂) = 2(m₁m₂)

`-8/5 = 2("a"/5)`

a = −4