The distance between the points (a cos θ + b sin θ, 0) and (0, a sin θ – b cos θ), is
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Answer:
Step-by-step explanation:
Given the point A(cosθ+bsinθ,0),(0,asinθ−bcosθ)
By distance formula,
The distance of AB=
(x
2
−x
1
)
2
+(y
2
−y
1
)
2
=
[0−(acosθ+bsinθ)
2
+(asinθ−bcosθ)−0]
2
=
a
2
cos
2
θ+2abcosθsinθ+a
2
sin
2
θ+b
2
cos
2
θ−2absinθcosθ
=
(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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