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```        hey i have few questions that i didnt know how to approach
1. A and B are two points(3,4)and(5,-2).Find the co-ordinates of a point such that PA=PB and area of triangle PAB=10
2.Find the equation of the path of a point such that the sum of its distances from the points(0,3)and(0,-3)is 8
3.Find the ratio in which the line segment joining the points (2,3)and (4,5) is divided by the line joining the points (6,8) and (-3,-2)
4.Find the equation of the bisector of angle A of the triangle whose vertices are A(4,3) B(0,0) and C(2,3)
5.Through the point P(3,-5) a line is drawn inclined at 45degree with the positive x-axis.It meets the line x+y-6=0 at the point Q.Find the length PQ
```
8 years ago

## Answers : (1)

```							Dear student,
Let co-ordinates of P be (   ), then PA = PB  PA2=PB2 ( −1)2+( −2)2=( −3)2+( −8)2 −2 +1−4 +4=−6 +9−16 +64 4 +12 =68  +3 =17           ...(i)
Also area of PAB=10 21 (2 +8+3 )−( +6+8  =10  −6 +2 +2 =20  −3 + +1 =10 −3 + +1=10or -10 −3 + =9            ...(ii)   or    −3 + =−11        ...(iii)
Solving (i) and (ii), we get               |    Solving (i) and (iii), we get =−1  =6                              | =5  =4
Hence the points is either (-1,6) or (5,4).

Area of the quadrilateral formed by the given points
=21 (−35+4+4−6)−(−8−7+3+20) =21 −33−8 =21 −41 =142 square units.

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Sagar Singh
B.Tech, IIT Delhi

```
8 years ago
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