Find that distance between the piloints (acos0+bsin0,0) and (0,asin0-bcos0)
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The distance between the points
(
a
cos
θ
+
b
sin
θ
,
0
)
a
n
d
(
0
,
a
sin
θ
−
b
cos
θ
)
is _____.
A
a
2
+
b
2
B
a
+
b
C
a
2
−
b
2
D
√
a
2
+
b
2
Solution
Given the point
A
(
cos
θ
+
b
sin
θ
,
0
)
,
(
0
,
a
sin
θ
−
b
cos
θ
)
By distance formula,
The distance of
A
B
=
√
(
x
2
−
x
1
)
2
+
(
y
2
−
y
1
)
2
=
√
[
0
−
(
a
cos
θ
+
b
sin
θ
)
2
+
(
a
sin
θ
−
b
cos
θ
)
−
0
]
2
=
√
a
2
cos
2
θ
+
2
a
b
cos
θ
sin
θ
+
a
2
sin
2
θ
+
b
2
cos
2
θ
−
2
a
b
sin
θ
cos
θ
=
√
(
a
2
+
b
2
)
cos
2
θ
+
(
a
2
+
b
2
)
sin
2
θ
=
√
a
2
+
b
2
[
∵
cos
2
θ
+
sin
2
θ
=
1
]
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