Circle And System Of Circles Question 156
Question: The equation of the circle passing through the point (2, 1) and touching y-axis at the origin is
Options:
A) $ x^{2}+y^{2}-5x=0 $
B) $ 2x^{2}+2y^{2}-5x=0 $
C) $ x^{2}+y^{2}+5x=0 $
D) None of these
Show Answer
Answer:
Correct Answer: B
Solution:
We have the equation of circle $ x^{2}+y^{2}+2gx+2fy+c=0 $ But it passes through (0, 0) and (2, 1), then $ c=0 $ ………….(i) $ 5+4g+2f=0 $ ………….(ii)
Also $ \sqrt{g^{2}+f^{2}-c}=\ |g| $
therefore $ f=0 $
$ {\because \ c=0} $
From (ii), $ g=-\frac{5}{4} $
Hence the equation will be $ 2x^{2}+2y^{2}-5x=0 $ .
BETA
