# 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.

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 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).

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