Question

31. If x= h + a cos 0 and y = k + a sin 0, prove that (x - h)2 + (y - k)2 = a2​

Answer 1

Step-by-step explanation:

Given,

x=h+acosθ

y=k+asinθ

Now,

x−h=acosθ

y−k=asinθ

On squaring and adding we get,

(x−h)

2

+(y−k)

2

=a

2

cos

2

θ+a

2

sin

2

θ

=a

2

(sin

2

θ+cos

2

θ)

=a

2

(1) Since [sin

2

θ+cos

2

θ=1].

Hence proved.

Answer 2

Answer:

Step-by-step explanation:

Answer

Given,  

x=h+acosθ    

y=k+asinθ  

Now,

x−h=acosθ

y−k=asinθ

On squaring and adding we get,

(x−h)  

2

+(y−k)  

2

=a  

2

cos  

2

θ+a  

2

sin  

2

θ

=a  

2

(sin  

2

θ+cos  

2

θ)

=a  

2

(1)       Since  [sin  

2

θ+cos  

2

θ=1].  

Hence proved.