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. $\left( \frac { a } { 2 } , \frac { b } { 2 } \right)$
• D. $\left( \frac { b } { 2 } , - \frac { a } { 2 } \right)$

Answer 1

Answer: (C)

$\left( \frac { a } { 2 } , \frac { b } { 2 } \right)$

Answer 2

Let the equation of circle be

$x ^ { 2 } + y ^ { 2 } + 2 g x + 2 f y + c = 0$. Now on passing through the points, we get three equations.

$c = 0$ ….(i)

$a ^ { 2 } + 2 g a + c = 0$ ….(ii)

$b ^ { 2 } + 2 f b + c = 0$ ….(iii)

On solving them, we get

$g = - \frac { a } { 2 } , f = - \frac { b } { 2 }$

Hence the centre is $\left( \frac { a } { 2 } , \frac { b } { 2 } \right)$.