Question

A straight line passing through A(-2, 1) makes an angle of 30° with OX in the positive
direction. Find the points on the straight line whose distance from A is 4 units.​

Answer 1

A straight line passing through A(-2 , 1) makes an angle of 30° with OX in the positive direction.

To find : The points on the straight line whose distance from A is 4 units.

solution : slope of the line passing through A(-2,1) = tan30°

⇒(y - 1)/(x + 2) = 1/√3

⇒y - 1 = 1/√3 (x + 2)

⇒√3y - √3 = x + 2

⇒x - √3y + 2 + √3 = 0

now the points on the straight line whose distance from A is 4 units are ; (-2 ± 4cos30°, 1 ± 4sin30°) = (-2 ± 2√3 , 1 ± 2)

= (-2 + 2√3, 3) or (-2 - 2√3, -1)

Therefore the points on the straight of which distance from A is 4 units are (-2 + 2√3, 3) or (-2 - 2√3, -1)