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