Anaytical Geomety



Find the equation of the line whose gradient is

 and which passes through 



, where 



 divides the line segment joining 



 and 



 in the ratio 



 internally.

[3]

2)

Find the angle between the straight lines:










[2]

3)

An object was launched from place



 at constant speed to hit a target. At the 



 second, it was 



 away from the target, and 



 away at the 



 second.


[4]

A)

Find the distance between the place and the target.

[2]

B)

Find the distance covered by it in 15 seconds.

[1]

C)

Find the time taken to hit the target.

[1]

4)

Find the area of the triangle formed by the vertices



.

[3]

5)

Find the equations of bisectors of the angle between the axes.

[2]

6)

Find the distance between the parallel lines



.

[2]

7)

Find equations of the bisector of the angles between the lines



.
Also determine the condition that the bisector of the angle in which the origin lies.

[5]

8)

Find the equations of the internal bisectors of the angles of the triangle whose sides are



. Also find the incenter of the triangle.

[5]

9)

Do the points



 lie on the same side of 



? Give the reason.

[1]

10)

If the length of the perpendicular from the point



 to the line 



 is 1, then 





[2]

11)

Find the equation of the straight line which makes equal intercepts on the axes and passes through the point of intersection of the lines



.





[4]

12)

Find the equation of the line passing through the middle point of the line segment connecting



 and parallel to the line 



.






[2]

13)

Find the value of



, if the lines 



 are parallel.

[2]

14)

If the points



 are collinear, then find the relation between 



.

[2]

15)

Find the equation of bisectors of the angles between the lines



. And prove that the bisectors are at right angles to each other.

[5]

16)

If



 and 



 are two vertices of a 



, then find the equation of a straight line that lies along the diagonal BD.






[3]

17)

Find the perimeter of a triangle with vertices



.

[2]

18)

If



 is the length of perpendicular dropped from the 



 on line 



, prove that 



.

[3]

19)

Determine the equations of the bisectors of the angles between the lines



. Identify the bisectors of the acute angle.

[5]

20)

If the line segment joining the points



 and 



 subtends an angle 



 at origin. Find the 



.






[3]

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