Question

The perimeter of a triangle is 20 and the points (-2, -3) and (-2, 3) are two of the vertices of it.  Then the locus of third vertex is :

Answer 1

Answer:

Step-by-step explanation:

Let the coordinates of the third vertex be A:(x,y)

Given that perimeter is 20

The other two vertices given are B:(−2,−3) and C:(−2,3)

We know that Perimeter =AB+AC+BC  ........(1)

Using distance formula, we get

⇒AB=  

(x+2)  

2

+(y+3)  

2

 

​  

 

⇒AC=  

(x+2)  

2

+(y−3)  

2

 

​  

 

⇒BC=  

36

​  

=6

Putting these values in (1), we get  

(x+2)  

2

+(y+3)  

2

 

​  

+  

(x+2)  

2

+(y−3)  

2

 

​  

=20−6=14

⇒  

(x+2)  

2

+(y+3)  

2

 

​  

=14−  

(x+2)  

2

+(y−3)  

2

 

​  

 

Squaring both sides, we get

⇒(x+2)  

2

+(y+3)  

2

=196+(x+2)  

2

+(y−3)  

2

−28  

(x+2)  

2

+(y−3)  

2

 

​  

 

⇒12y−196=−28  

(x+2)  

2

+(y−3)  

2

 

​  

 

⇒49−3y=7  

(x+2)  

2

+(y−3)  

2

 

​  

 

Again squaring both sides, we get

⇒2401+9y  

2

−294y=49(x+2)  

2

+49y  

2

+441−294y

⇒1960=49(x+2)  

2

+40y  

2

 

⇒  

40

(x+2)  

2

 

​  

+  

49

y  

2

 

​  

=1