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find the equation of the set of points which are e
Question:
Find the equation of the set of points which are equidistant from the points (1, 2, 3) and (3, 2, –1).
CBSE Class XI
Updated On:
Oct 23, 2023
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Solution and Explanation
Let P (x, y, z) be the point that is equidistant from points A(1, 2, 3) and B(3, 2, -1).
Accordingly, PA = PB
⇒ PA
2
= PB
2
⇒(x-1)
2
+(y-2)
2
+(z−3)
2
= (x−3)
2
+(y−2)
2
+(z+1)
2
⇒ x
2
- 2x + 1+ y
2
- 4y+4+z
2
- 6z + 9 = x
2
- 6x+9+ y
2
- 4y+ 4 + z
2
+2z+1
⇒ - 2x - 4y - 6z +14= - 6x - 4y+ 2z+14
⇒ - 2x - 6z + 6x - 2z = 0
⇒ 4x - 8z = 0
⇒x - 2z= 0
Thus, the required equation is x - 2z = 0.
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