Circle And System Of Circles Question 94
Question: If a circle passes through the point (0, 0), (a, 0), (0, b), then its centre is
[MNR 1975]
Options:
A) $ (a,\ b) $
B) $ (b,\ a) $
C) $ ( \frac{a}{2},\ \frac{b}{2} ) $
D) $ ( \frac{b}{2},\ -\frac{a}{2} ) $
Show Answer
Answer:
Correct Answer: C
Solution:
Let the equation of circle be $ x^{2}+y^{2}+2gx+2fy+c=0 $ . Now on passing through the points, we get three equations. $ c=0 $ ………….(i) $ a^{2}+2ga+c=0 $ ………….(ii) $ b^{2}+2fb+c=0 $ ………….(iii) On
Solving them, we get $ g=-\frac{a}{2},\ f=-\frac{b}{2} $
Hence the centre is $ ( \frac{a}{2},\ \frac{b}{2} ) $ .
BETA
