Question

Which of the following is not common tangent to the circles $x^2+y^2-6x=0$ and $x^2+y^2+2x=0$?

• A. $x+\sqrt{3}y+3=0$
• B. $x-\sqrt{3}y+3=0$
• C. $x=0$
• D. $\sqrt{3}x-y+3=0$

Answer 1

Answer: (C)

$x=0$

Consider the given equations

$x^2+y^2-6x=0......\left(1\right)$

$x^2+y^2+2x=0......\left(2\right)$

Comparing that, general equation of circle and we get,

$x^2+y^2+2gx+2fy+c=0$

Then,

Centre (1) $(-g,-f)=(3,0)$ and $c=0$ then, Radius

$r_1=\sqrt{g^2+f^2-c}$

$=\sqrt{3^2+0^2-0}=3$

Centre (2) $(-g,-f)=(-1,0)$ and $c=0$ then, Radius

$r_2=1$

Note:- This point is the one dividing the line joining their centres in the ratio of their radii internally.

Here, using the section formula and we get,

Point of contact $(0,0)$.

We’ll get the equation of the line as $x=0$

Hence, this the answer.