Coordinate Geometry Question 123
Question: If sum of distances of a point from the origin and lines $ x=2 $ is 4, then its locus is
[RPET 1997]
Options:
A) $ x^{2}-12y=36 $
B) $ y^{2}+12x=36 $
C) $ y^{2}-12x=36 $
D) $ x^{2}+12y=36 $
Show Answer
Answer:
Correct Answer: B
Solution:
Let point be $ P(x,y) $ . So, distance from the origin $ OP=\sqrt{x^{2}+y^{2}} $ and distance from the line $ =(x-2) $
$ \therefore \sqrt{x^{2}+y^{2}}+(x-2)=4\Rightarrow \sqrt{x^{2}+y^{2}}=(-x+6) $
$ \Rightarrow x^{2}+y^{2}=x^{2}+36-12x\Rightarrow y^{2}+12x=36 $ .
BETA
