Question

The common tangents to the circles $x^2+y^2-6x=0$ and $x^2+y^2+2x=0$ is/are

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

Answer 1

Answer: (A), (B), (C)

The correct options are
A $x=0$
B $\sqrt{3}y=x+3$
C $\sqrt{3}y+x+3=0$

Using the section formulae we get $P\equiv (-3,0)$
Now angle made by the tangents to the $x-$axis is
$\sin \theta =\frac{1}{2}\Rightarrow \theta =30°$
So the equation of the tangents will be
$\sqrt{3}y=\pm (x+3)$ and $x=0$