Question

5.
The locus of the point x = a cos theta, y= b sin theta​

Answer 1

Answer:

Step-by-step explanation:

It is given that  

x=a(cosθ+sinθ)

y=b(cosθ−sinθ)

Now bx=ab(cosθ+sinθ) ...(i)

ay=ab(cosθ−sinθ) ...(ii)

Hence, b  

2

x  

2

+a  

2

y  

2

 

=a  

2

b  

2

(cos  

2

θ+sin  

2

θ+2cosθsinθ+cos  

2

θ+sin  

2

θ−2cosθsinθ)

=a  

2

b  

2

(2(cos  

2

θ+sin  

2

θ))

=2a  

2

b  

2

 

Hence, b  

2

x  

2

+a  

2

y  

2

=2a  

2

b  

2

 

Dividing the entire equation by a  

2

b  

2

 gives us

a  

2

 

x  

2

 

​  

+  

b  

2

 

y  

2

 

​  

=2

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Answer 2

Hope This Helps U ......