A line passes through a point A(1,2) and makes an angle of 60degree with x-axis and intersects line x+y=6 at point P.find AP.
Suppose the equation of line AP is y = mx + c
Since this line makes an angle of 60 degree with x-axis;
So the slope of line AP; m =
So the equation of line AP is
And this line passes through the point A(1, 2), so we have;
Therefore the equation of the line AP is ...(i)
The line AP intersects the line x + y = 6 i.e. y = 6 - x...(ii)
solving (i) and (ii) we get;
So intersection point is .
Using the distance formula to find the distance between the point A(1, 2) and , we have;
Therefore AP =