Question

Find the equation of a circle passes through the origin and centre lies on $x-$axis

• A. $x^2+y^2+ax=0$
• B. $x^2+y^2-2ya=0$
• C. $x^2+y^2-2xa=0$
• D. $x^2+y^2+ya=0$

Answer 1

Answer: (C)

$x^2+y^2-2xa=0$

If a circle passes through the origin and centre lies on $x$-axis then the abscissa will be equal to the radius of the circle and the $y$- co-ordinate of the centre will be zero. Hence, the equation of the circle will be of the form:

${(x-a)}^2+y^2=a^2$

$\Rightarrow x^2+a^2-2ax+y^2=a^2$

$\therefore x^2-2ax+y^2=0$ is the required equation of the circle