If the distance of P from points (2,3)(2, - 3) are in the ratio 2 :3. Find locus of P
Answers
Answered by
1
Step-by-step explanation:
Let the point P be (x,y)
The distance between the points (x,y),(2,3) is
(2−x)
2
+(3−y)
2
The distance between the points (x,y),(2,−3) is
(2−x)
2
+(−3−y)
2
Given that the distances are in the ratio of 2:3
Therefore,
(2−x)
2
+(−3−y)
2
(2−x)
2
+(3−y)
2
=
3
2
⟹
(2−x)
2
+(−3−y)
2
(2−x)
2
+(3−y)
2
=
9
4
⟹
4+x
2
−4x+9+y
2
+6y
4+x
2
−4x+9+y
2
−6y
=
9
4
⟹9(4+x
2
−4x+9+y
2
−6y)=4(4+x
2
−4x+9+y
2
+6y)
⟹36+9x
2
−36x+81+9y
2
−54y=16+4x
2
−16x+36+4y
2
+24y
⟹5x
2
+5y
2
−20x−78y+65=0
Therefore, the locus of the point P is 5x
2
+5y
2
−20x−78y+65=0
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Answered by
2
Answer:
5×2+5y2- 20 × -78y + 65 = 0.
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