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Byju's Answer
Standard X
Mathematics
Distance between Two Points on the Same Coordinate Axes
If co-ordinat...
Question
If co-ordinates of
P
and
Q
are
(
a
cos
θ
,
b
sin
θ
)
and
(
−
a
sin
θ
,
b
cos
θ
)
respectively , then show that
O
P
2
+
O
Q
2
=
a
2
+
b
2
,
where
O
is origin.
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Solution
P
=
(
a
cos
θ
,
b
sin
θ
)
Q
=
(
−
a
sin
θ
,
b
cos
θ
)
0
is the origin
∴
O
P
2
+
O
Q
2
=
[
√
(
0
−
a
cos
θ
)
2
+
(
0
−
b
sin
θ
)
2
]
2
+
[
√
(
0
+
a
cos
θ
)
2
+
(
0
−
b
sin
θ
)
2
]
2
=
a
2
cos
2
θ
+
b
2
sin
2
θ
+
a
2
sin
2
θ
+
b
2
cos
2
θ
=
a
2
[
cos
2
θ
+
sin
2
θ
]
+
b
2
[
cos
2
θ
+
sin
2
θ
]
=
a
2
+
b
2
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0
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