Question

If a circle passes through the point (0, 0), (a, 0), (0, b), then its centre is

• A. (a, b)
• B. (b, a)
• C. $(\frac{a}{2},\frac{b}{2})$
• D. $(\frac{b}{2},-\frac{a}{2})$

Answer 1

The correct option is C $(\frac{a}{2},\frac{b}{2})$

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 $(\frac{a}{2},\frac{b}{2})$.