Question

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. $\lambda =0$

Answer 1

Answer: (A)

$\lambda >0$

Given,

$y^2=4x$

represents the right side opening parabola

$x^2+y^2+2\lambda x=0$

represents a circle.

if $\lambda >0\Rightarrow \lambda =1$

$x^2+y^2+2x=0$

represents a circle, $C(-1,0)$ externally touching the parabola

if $\lambda <0\Rightarrow \lambda =-1$

$x^2+y^2-2x=0$

represents a circle, $C(1,0)$ internally touching the parabola

if $\lambda =0\Rightarrow \lambda =0$

$x^2+y^2=0$

represents a circle, $C(0,0)$ on parabola