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Standard XII
Mathematics
Distance Formula
Question
The point
P
is on the
y
-axis. If
P
is equidistant from
(
1
,
2
,
3
)
and
(
2
,
3
,
4
)
, then
P
y
=
15
2
15
30
3
2
A
15
2
B
30
C
15
D
3
2
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Solution
Verified by Toppr
Let the point be
(
0
,
y
,
0
)
Since, it is equidistant from the
2
points.
⇒
(
1
+
(
y
−
2
)
2
+
9
)
=
(
4
+
(
y
−
3
)
2
+
16
)
⇒
(
10
+
y
2
−
4
y
+
4
)
=
(
20
+
y
2
−
6
y
+
9
)
⇒
y
2
−
4
y
+
14
=
y
2
−
6
y
+
29
⇒
2
y
=
15
⇒
y
=
15
2
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