Coordinate Geometry Question 106
Question: The locus of the moving point P, such that 2PA = 3PB where A is (0,0) and B is (4,-3), is
[AMU 1980]
Options:
A) $ 5x^{2}-5y^{2}-72x+54y+225=0 $
B) $ 5x^{2}-5y^{2}+72x+54y+225=0 $
C) $ 5x^{2}+5y^{2}+72x+54y+225=0 $
D) $ 5x^{2}+5y^{2}-72x+54y+225=0 $
Show Answer
Answer:
Correct Answer: D
Solution:
Let $ P(h,k). $ Given $ 2PA=3PB\Rightarrow 4PA^{2}=9PB^{2} $
$ \Rightarrow 4(h^{2}+k^{2})=9[{{(h-4)}^{2}}+{{(k+3)}^{2}}] $
$ \Rightarrow 5h^{2}+5k^{2}-72h+54k+225=0 $
Hence the locus of point P is given by $ 5x^{2}+5y^{2}-72x+54y+225=0 $ .
BETA
