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

Dear student,

Let co-ordinates of P be (), then

PA=PBPA2=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.

Please feel free to ask your queries here. We are all IITians and here to help you in your IIT JEE preparation.

All the best.

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B.Tech, IIT Delhi