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Tardigrade
Question
Mathematics
A point P moves in such a way that sum of its perpendicular distances from two perpendicular lines in its plane is always 2 units. Then find the area of region bounded by locus of P .
Q. A point
P
moves in such a way that sum of its perpendicular distances from two perpendicular lines in its plane is always
2
units. Then find the area of region bounded by locus of
P
.
106
111
NTA Abhyas
NTA Abhyas 2022
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Answer:
8
Solution:
Let
x
axis and
y
axis be the two perpendicular lines. Let
P
be
(
h
,
k
)
then
∣
h
∣
+
∣
k
∣
=
2
So locus of
P
is
⇒
∣
x
∣
+
∣
y
∣
=
2
Which represents four lines forming a square
Area
=
4
(
2
1
⋅
2
⋅
2
)
=
8
sq. units