Q. 14.2( 6 Votes )

# 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.

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)

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