Question

The line 5x + y – 1 = 0 coincides with one of the lines given by 5x² + xy – kx – 2y + 2 = 0 then the value of k is ______.

Options

• –11

• 31

• 11

• –31

Answer 1

The line 5x + y – 1 = 0 coincides with one of the lines given by 5x² + xy – kx – 2y + 2 = 0 then the value of k is 11.

Explanation:

5x + y – 1 = 0

5x² + xy – kx – 2y + 2 = 0

∴ a = 5, b = 0, h = `1/2`, g = `-k/2`, f = –1, c = 2

If the above equation represents a pair of straight lines, then

`|(a, h, g),(h, b, f),(g, f, c)|` = 0

`\implies |(5, 1/2, -k/2),(1/2, 0, -1),(-k/2, -1, 2)|` = 0

∴ `5(0 - 1) - 1/2(1 - k/2) - k/2((-1)/2 - 0)` = 0

∴ `-5 - 1/2 + k/4 + k/4` = 0

`\implies k/2 = 11/2`

`implies` k = 11