Question

The equation to the circle passing through $(0,0),(1,0)$ and touching the circle $x^2+y^2=9$

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

Answer 1

The correct option is A $x^2+y^2-x-2\sqrt{2}y=0$

Let $x^2+y^2+2gx+2fy=0$ circle passing through $(0,0)$
and also pass through $(1,0)$
so, 1+2g=0$\Rightarrow g=-\frac{1}{2}$
and this circle touche $x^2+y^2=9$ internally
so, $|r_1-r_2|=c_1{c}_2$
$3-\sqrt{g^2+f^2}=\sqrt{g^2+f^2}$
$g^2+f^2=\frac{9}{4}$
$f^2=2$
$f=\pm \sqrt{2}$
so, $e{q}^n$ of circle is
$x^2+y^2+x\pm 2\sqrt{2}y=0$