Question

The circle $x^2+y^2+2\lambda x=0,\lambda ϵR,$ touches the parabola $y^2=4x$ externally. Then

• A. $\lambda >0$
• B. $\lambda <0$
• C. $\lambda >1$
• D. none of these

Answer 1

The correct option is A $\lambda >0$

Centre of the circle is $(-\lambda ,0)$ and its radius is $\lambda$
Clearly centre of the circle is on the axis of the parabola. Thus for both curve to touch externally only centre of the circle should be on the left side of the origin $\Rightarrow \lambda >0$. Circle and parabola will meet at the the vertex of the parabola.