Question

If one of the lines given by kx² + 2xy – 3y² = 0 is perpendicular to the line 3x + 5y+ 1 = 0, then the value of k is ______.

Options

• 3

• `-7/2`

• `-3/5`

• 5

Answer 1

If one of the lines given by kx² + 2xy – 3y² = 0 is perpendicular to the line 3x + 5y+ 1 = 0, then the value of k is 5.

Explanation:

Given equation of pair of lines is

kx² + 2xy – 3y² = 0 

⇒ `"k" + 2(y/x) - 3(y/x)^2` = 0

⇒ kx² + 2m – 3m² = 0  ......(i)

Now, slope of line 3x + 5y + 1 = 0 is m₁ = `(-3)/5`.

∴ Slope of the line perpendicular to 3x + 5y + 1 = 0 is m = `5/3`.

Substituting the value of m in (i), we get

`"k" + 2(5/3) - 3(5/3)^2` = 0

⇒ k = 5