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 :
Answers
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