Question

A is a point (1, 3, 4) and B is the point (1, -2, -1). A point P (x, y) moves so that 3PA = Find the relation between x and y.​

Answer 1

Answer:

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Class 11

>>Maths

>>Introduction to Three Dimensional Geometry

>>Distance between Two Points

>>P is a variable point which moves such t

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P is a variable point which moves such that 3PA=2PB. If A=(−2,2,3) and B=(13,−3,13) prove that P satisfies the equation x

2

+y

2

+z

2

+28x−12y+10z−247=0.

Medium

Solution

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Let P=(x,y,z)

PA=

(x−(−2))

2

+(y−2)

2

+(z−3)

2

PB=

(x−13)

2

+(y−(−3))

2

+(z−13)

2

given that 3PA=2PB

3

(x+3)

2

+(y−2)

2

+(z−3)

2

=2

(x−13)

2

+(y+3)

2

+(z−13)

2

9[(x+3)

2

+(y−2)

2

+(z−3)

2

]=4[(x−13)

2

+(y+3)

2

+(z−13)

2

]

on solving this we get x

2

+y

2

+z

2

+28x−12y+10z−247=0