Question

Let L be the line joining the origin to the point of intersection of the lines represented by 2x² – 3xy – 2y² + 10x + 5y = 0. lf L is perpendicular to the line kx + y + 3 = 0, then k = ______.

Options

• `1/2`

• `(-1)/2`

• –1

• `1/3`

Answer 1

Let L be the line joining the origin to the point of intersection of the lines represented by 2x² – 3xy – 2y² + 10x + 5y = 0. lf L is perpendicular to the line kx + y + 3 = 0, then k = `(-1)/2`.

Explanation:

Given equation of pair of lines is

2x² – 3xy – 2y² + 10x + 5y = 0

∴ a = 2, b = –2, c = 0, f = `5/2`, g = 5, h = `(-3)/2`

∴ Point of intersection of the lines is

`(("hf" - "bg")/("ab" - "h"^2), ("gh" - "af")/("ab"  ""^2)) = (-1, 2)`

Slope of line L joining origin and (–1, 2) is m = –2

Slope of k.x + y + 3 = 0 is –k

Now, (–k)(–2) = –1

⇒ `(-1)/2`