Coordinate Geometry Question 57
Question: The locus of a point P which moves in such a way that the segment OP, where O is the origin, has slope $ \sqrt{3} $ is
Options:
A) $ x-\sqrt{3}y=0 $
B) $ x+\sqrt{3}y=0 $
C) $ \sqrt{3}x+y=0 $
D) $ \sqrt{3}x-y=0 $
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Answer:
Correct Answer: D
Solution:
Slope is given by $ \frac{dy}{dx}=\sqrt{3}\Rightarrow \int _{{}}^{{}}{dy}=\sqrt{3}\int _{{}}^{{}}{dx} $
$ \Rightarrow \sqrt{3}x-y+c=0 $ This passes through (0, 0), so c = 0
Hence the required locus is $ \sqrt{3}x-y=0 $ .
BETA
