Question

The distance between the points (acoso+bsineo, 0)and (0,asineo-bcoso)is​

Answer 1

Answer:

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]

Step-by-step explanation: