Circle And System Of Circles Question 145
Question: The equation of the circle passing through the points (0, 0), (0, b) and (a, b) is
[AMU 1978]
Options:
A) $ x^{2}+y^{2}+ax+by=0 $
B) $ x^{2}+y^{2}-ax+by=0 $
C) $ x^{2}+y^{2}-ax-by=0 $
D) $ x^{2}+y^{2}+ax-by=0 $
Show Answer
Answer:
Correct Answer: C
Solution:
Equation of circle passing through (0, 0) is $ x^{2}+y^{2}+2gx+2fy=0 $ ………….(i)
Also, circle (i) is passing through (0, b) and (a, b)
$ \therefore $ $ f=-\frac{b}{2} $ and $ a^{2}+b^{2}+2ag+2( -\frac{b}{2} )\text{ }b=0 $
$ \Rightarrow g=-\frac{a}{2} $
Hence the equations of circle is, $ x^{2}+y^{2}-ax-by=0 $ .
BETA
