Question

Circles are drawn through the point $(-5,0)$ to cut the x-axis on the positive side and making an intercept of $10$ units on the x-axis. The equation of the locus of the center of these circle is

• A. $x+y=0$
• B. $x-y=0$
• C. $x=0$
• D. $y=0$

Answer 1

The correct option is C $x=0$

Since the circles pass through $(-5,0)$ and makes an intecept of $10$ units on the positive side of the x-axis,

it also passes though $(5,0)$

$\therefore$ If $C(x,y)$ is the center of such circle

${(x+5)}^2+y^2={(x-5)}^2+y^2$ $(\because CA=CB=$ radius $)$

$\Rightarrow x=0$