Question

Find the points on the X – axis whose distances from the points A (7, 6) and B (-3, 4) are in the ratio 1: 2?

Answer 1

Answer:

Let (x,y) be the req. point on y axis be (0,y)

given points A(6,7)B(4,−3)

A=

(0−6)

2

+(y−7)

2

OB=

(0−4)

2

+(y+3)

2

OB

OA

=

2

1

2OA=OB

4OA

2

=OB

4[(6)

2

+(y+7)

2

]=(4)

2

+(y+3)

2

4[36+y

2

+49−14y]=4

2

+y

2

+9+6y

y

2

+6y+25

4y

2

−56y+340

3y

2

−62y+315=0

3y

2

−27y−35y+315=0

3y(y−9)−35(y−9)=0

(3y−35)(y−9)=0

y=

3

35

y=9

point (0,9) ( 0,35/3 )