# 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

SAGAR SINGH - IIT DELHI
878 Points
13 years ago

Dear student,

Let co-ordinates of P be (), then

PA=PBPA2=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=203++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)

=21338=2141

=142 square units.

All the best.

Win exciting gifts by answering the questions on Discussion Forum. So help discuss any query on askiitians forum and become an Elite Expert League askiitian.