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# hey i have few questions that i didnt know how to approach1. 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=102.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 83.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

## 1 Answers

10 years ago

Dear student,

Let co-ordinates of P be (   ), then PA = PB  PA2=PB2 ( 1)2+( 2)2=( 3)2+( 8)2 2 +14 +4=6 +916 +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+46)(87+3+20) =21 338 =21 41 =142 square units.

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