A line passes through a point A (1, 2) and makes an angle of 60⁰ with the x–axis and intercepts the line x + y = 6 at the point P. Find AP.

Question

A line passes through a point A (1, 2) and makes an angle of 60 0 with the x–axis and intercepts the line x + y = 6 at the point P. Find AP.

Philoid · Accepted Answer

Given: (x₁,y₁) = A(1, 2), θ = 60°

To find:

Distance AP.

Explanation:

So, the equation of the line is

Formula Used:

⇒

Here, r represents the distance of any point on the line from point A (1, 2).

The coordinate of any point P on this line are

Clearly, P lies on the line x + y = 6

⇒ 1 + + 2 + = 6

⇒ = 3

⇒ r (√3 + 1) = 6

⇒ r =

Therefore, AP = 3(√3 – 1)

A line passes through a point A (1, 2) and makes an angle of 600 with the x–axis and intercepts the line x + y = 6 at the point P. Find AP.