# The given circle #x^2 + y^2 + 2px = 0#, #p inRR# touches the parabola #y^2 = 4x# externally, then( prove this mathematically)?

##
A)#p<0#

B)#p>0#

C)#0<p<1#

D)#p<-1#

The answer is B) for your reference.

A)

B)

C)

D)

The answer is B) for your reference.

##### 1 Answer

Jan 31, 2018

Answer is (B)

#### Explanation:

The parabola

Further, equation of circle

Therefore, the circle will touch the parabola externally if centre is

If

Below we show three circles touching parabola externally if

graph{(x^2+y^2+x)(x^2+y^2+8x)(x^2+y^2+4x)(x^2+y^2-4x)(y^2-4x)=0 [-9.83, 10.17, -4.965, 5.035]}

Hence, answer is (B).