Question

Find the equation of locus of a point p is the distance of Puri from a into 30 is twice then distance of p from b - 30

Answer 1

Answer:

Step-by-step explanation:

Let the point P be (x,y)

The distance between P(x,y) and A(3,0) is  

(3−x)  

2

+(0−y)  

2

 

​  

 

The distance between P(x,y) and B(−3,0) is  

(−3−x)  

2

+(0−y)  

2

 

​  

 

Given that PA=2PB

⟹  

(3−x)  

2

+y  

2

 

​  

=2  

(−3−x)  

2

+y  

2

 

​  

 

squaring on both sides

⟹(3−x)  

2

+y  

2

=4((−3−x)  

2

+y  

2

)

⟹9+x  

2

−6x+y  

2

=4(9+x  

2

+6x+y  

2

)

⟹9+x  

2

−6x+y  

2

=36+4x  

2

+24x+4y  

2

 

⟹3x  

2

+3y  

2

+30x+27=0

Therefore, the locus of the point P is 3x  

2

+3y  

2

+30x+27=0