Question -
Answer -
Given:
(x1, y1)= A (4, -1)
Let us findCoordinates of the two points on this line which are at a distance of 5 unitsfrom A.
Given: Line 3x – 4y +1 = 0
4y = 3x + 1
y = 3x/4 + 1/4
Slope tan θ = 3/4
So,
Sin θ = 3/5
Cos θ = 4/5
The equation of theline passing through A (4, −1) and having slope ¾ is
By using the formula,
The equation of theline is given by:
3x – 4y = 16
Here, AP = r = ± 5
Thus, the coordinatesof P are given by
x
= ±4 + 4 and y = ±3 –1
x = 8, 0 and y = 2, –4
∴ The coordinates ofthe two points at a distance of 5 units from A are (8, 2) and (0, −4).