Question

Find the locus of the mid point of the portion of the line xcosA+ysinA=p
intercepted between the axes?

Answer 1

Let the line cut the axes in A and B and if (h,k) be the midpoints of AB, then

2h=  

cosθ

p

​

,2k=  

sinθ

p

​

 

In order to find the locus, eliminate the variable θ by cos  

2

θ+sin  

2

θ=1

x  

2

 

1

​

+  

y  

2

 

1

​

=  

p  

2

 

4

​

hope it will helps

Answer 2

Answer:

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Step-by-step explanation:

Let the line cut the axes in A and B and if (h,k) be the midpoints of AB, then

2h=

cosθ

p

,2k=

sinθ

p

In order to find the locus, eliminate the variable θ by cos

2

θ+sin

2

θ=1

x

2

1

+

y

2

1

=

p

2

4