Question

If the circle $x^2+y^2+2\lambda x=0,\lambda \in R$ touches the parabola $y^2=4x$ externally, then

• A. $\lambda >0$
• B. $\lambda <0$
• C. $\lambda >1$
• D. $\lambda <1$

Answer 1

The correct option is A $\lambda >0$

Center of the circle is $(-\lambda ,0)$ and its radius is $\lambda$
Clearly center of the circle is on the axis of the parabola.
Thus for both curves to touch externally,center of the circle should be on the left side of the origin
$\Rightarrow \lambda >0$