Question

The distance between the points
( a cos teta +b sin teta, 0 and ( 0, sin teta - b cos teta )​

Answer 1

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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