Circle And System Of Circles Question 236
Question: The locus of the middle points of chords of the circle $ x^{2}+y^{2}-2x-6y-10=0 $ which passes through the origin, is
[Roorkee 1989]
Options:
A) $ x^{2}+y^{2}+x+3y=0 $
B) $ x^{2}+y^{2}-x+3y=0 $
C) $ x^{2}+y^{2}+x-3y=0 $
D) $ x^{2}+y^{2}-x-3y=0 $
Show Answer
Answer:
Correct Answer: D
Solution:
Let the midpoint of chord be (h, k), then its equation is $ T=S_1 $ i.e., $ {{(p-x)}^{2}}=4qy $
$ =h^{2}+k^{2}-2h-6k-10 $
Since it passes through the origin, therefore $ h^{2}+k^{2}-h-3k=0 $ or locus is $ x^{2}+y^{2}-x-3y=0 $ .
BETA
