Question

The equation of the circle passing through the points (0, 0), (0, b) and (a, b) is.

• A. $x ^ { 2 } + y ^ { 2 } + a x + b y = 0$
• B. $x ^ { 2 } + y ^ { 2 } - a x + b y = 0$
• C. $x ^ { 2 } + y ^ { 2 } - a x - b y = 0$
• D. $x ^ { 2 } + y ^ { 2 } + a x - b y = 0$

Answer 1

Answer: (C)

$x ^ { 2 } + y ^ { 2 } - a x - b y = 0$

Answer 2

Equation of circle passing through (0, 0) is

$x ^ { 2 } + y ^ { 2 } + 2 g x + 2 f y = 0$ ….(i)

Also, circle (i) is passing through (0, b) and (a, b)

$\therefore$ $f = - \frac { b } { 2 }$ and $a ^ { 2 } + b ^ { 2 } + 2 a g + 2 \left( - \frac { b } { 2 } \right) b = 0$

$\Rightarrow g = - \frac { a } { 2 }$

Hence the equations of circle is, $x ^ { 2 } + y ^ { 2 } - a x - b y = 0$.