A line a drawn through A (4, – 1) parallel to the line 3x – 4y + 1 = 0. Find the coordinates of the two points on this line which are at a distance of 5 units from A.

Question

Philoid · Accepted Answer

Given: (x₁,y₁) = A(4, – 1)

To find:

Coordinates of the two points on this line which are at a distance of 5 units from A.

Explanation:

Line 3x – 4y + 1 = 0

⇒ 4y = 3x + 1

⇒ y

Slope

⇒ sin θ and cos θ

So, the equation of the line passing through A (4, −1) and having slope is

Formula Used:

⇒

⇒ 3x – 4y = 16

Here, AP = r = ± 5
Thus, the coordinates of P are given by

⇒

⇒ x and y

⇒ x= ±4 + 4 and y = ±3–1

So x = 8, 0 and y = 2, – 4

Hence, the coordinates of the two points at a distance of 5 units from A are (8, 2) and (0, −4).