Question

A straight line passes through a point A (1, 2) and makes an angle 60owith the x-axis. This line intersects the line x + y = 6 at the point P. find AP.

Solution

Correct option is

Let required line be  

∴ P is (1 + cos 60o, 2 + r sin 60o) which lies on x + y = 6  

  

   

                                                                          

SIMILAR QUESTIONS

Q1

All chords of the curve 3x2 – y2 –2x + 4y = 0 that subtends a right angle at the origin, pass through a fixed point whose co-ordinate is –

Q2

In a triangle ABC,  and point A lies on line y = 2x + 3 where  Area of  is such that [∆] = 5. Possible co-ordinates of ∆ is/are –

Q3

 then the point (x, y) lies on same side of the line 2x + y – 6 = 0 as the point –

Q4

Find the area of the quadrilateral with vertices (3, 3), (1, 4), (–2, 1), (2, –3).

 

Q5

A straight line segment of length ‘p’ moves with its ends on two mutually perpendicular lines. find the locus of the point which divides the line in the ratio 1:2.

Q6

Find the acute angle between the two lines with slopes 1/5 and 3/2.

Q7

If a line has a slope = ½ and passes through (–1, 2); find its equation. 

Q8

If a line has a slope 1/2 and cuts off along the positive y-axis of length 5/2 find the equation of the line.

Q9

If a line passes through two points (1, 5) and (3, 7) find its equation.

Q10

Find the equation of the straight line, which passes through the point (3, 4) and whose intercept on y-axis is twice that on x-axis.