Question

A circle passes through $(0,0),(a,0)$ and $(0,b)$ the co-ordinate of its centre are

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

Answer 1

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

Equation of circle, given point $(0,0)\to c=0$

Equation of circle, given point $(a,0)\to a^2+2ga+c=0\to a(a+2g)=0\Rightarrow g=-\frac{a}{2}$

Equation of circle, given point $(0,b)\to b(b+2f)=0\Rightarrow f=-\frac{b}{2}$

Center of circle $=(-g,-f)=(\frac{a}{2},\frac{b}{2})$