Question

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

Answer 1

Step-by-step explanation:

Equation of line

y-1 = 1/(3)^1/2.(x+2)

x+2 = (3)^1/2.y - (3(^1/2

x - (3)^1/2.y +(2 +3^1/2) =0……………(1)

Let P(h,k) is a point on line (1) which is at

a distance of 4 units from A

AP = 4

or AP^2 = 16

(h+2)^2 + (k-1)^2 = 16…………….(2)

P lies on line (1)

h- (3)^1/2.k +(2+3^1/2) = 0………………..(3)

from eq.(3) put h + 2= (3)^1/2.(k - 1 ) in eq.(2).

or {3^1/2(k-1)}^2 +(k-1)^2 = 16

or 3.(k-1)^2+(k-1)^2 = 16

or 4.(k-1)^2 = 16

or (k-1)^2= 4

or k-1 =+/-2=> k = 1+/-2

or k = 3 or -1

but h=3^1/2.(k-1)-2 , put k=3

h=3^1/2(3–1)-2 =2(3^1/2- 1)

put k = -1

h=3^1/2(-1–1) - 2 = -2(3^1/2 + 1).

Required points are:-

{2(3^1/2–1) , 3 } and {-2(3^1/2 + 1) , -1 }