NCERT Class XI Mathematics - Introduction to Three Dimensional Geometry - Solutions
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Question : 8
Total: 20
Find the equation of the set of points which are equidistant from the points (1, 2, 3) and (3, 2, –1).
Solution:
Let A(x, y, z) be any point which is equidistant from points B(1, 2, 3) and C(3, 2, –1).
Then AB =√ ( x − 1 ) 2 + ( y − 2 ) 2 + ( z − 3 ) 2
AC =√ ( x − 3 ) 2 + ( y − 2 ) 2 + ( z + 1 ) 2
It is given that AB = AC
√ ( x − 1 ) 2 + ( y − 2 ) 2 + ( z − 3 ) 2 √ ( x − 3 ) 2 + ( y − 2 ) 2 + ( z + 1 ) 2
⇒( x − 1 ) 2 + ( y − 2 ) 2 + ( z − 3 ) 2 ( x − 3 ) 2 + ( y − 2 ) 2 + ( z + 1 ) 2
⇒x 2 z 2 x 2 z 2
⇒ - 2x - 6z + 10 = - 6x + 2z + 10 ⇒ - 2x - 6z + 6x - 2z = 0
⇒ 4x - 8z = 0 ⇒ x - 2z = 0
Then AB =
AC =
It is given that AB = AC
⇒
⇒
⇒ - 2x - 6z + 10 = - 6x + 2z + 10 ⇒ - 2x - 6z + 6x - 2z = 0
⇒ 4x - 8z = 0 ⇒ x - 2z = 0
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