Question

Let the perpendiculars from any point on the line 7x + 56y = 0 upon 3x + 4y = 0 and 5x – 12y = 0 be p and p', then ______.

Options

• 2p = p'

• p = 2P'

• p = p'

• None of these

Answer 1

Let the perpendiculars from any point on the line 7x + 56y = 0 upon 3x + 4y = 0 and 5x – 12y = 0 be p and p', then p = p'.

Explanation:

Any point on the line 7x + 56y = 0 is

`(x_1, - (7x_1)/56), i.e., (x_1, - x_1/8)`

∴ The perpendicular distance p and p' are

p = `(3x_1 - (4x_1)/8)/5 = x_1/2` and p' = `(5x_1 - (12x_1)/8)/13 = x_1/2`

`\implies` p = p'