Coordinate Geometry Question 84
Question: The coordinates of the points O, A and B are (0,0), (0,4) and (6,0) respectively. If a points P moves such that the area of $ \Delta POA $ is always twice the area of $ \Delta POB $ , then the equation to both parts of the locus of P is
[IIT 1964]
Options:
A) $ (x-3y)(x+3y)=0 $
B) $ (x-3y)(x+y)=0 $
C) $ (3x-y)(3x+y)=0 $
D) None of these
Show Answer
Answer:
Correct Answer: A
Solution:
The three given points are $ O(0,0),A(0,4) $ and $ B(6,0) $ and let $ P(x,y) $ be the moving point. Area of $ \Delta POA=2. $ Area of $ \Delta POB $
$ \Rightarrow \frac{1}{2}\times 4\times x=\pm 2\times \frac{1}{2}\times 6\times y $ or $ x=\pm 3y $
Hence the equation to both parts of the locus of P is $ (x-3y)(x+3y)=0 $ .
BETA
