JEE Mains Model Paper 8

Focus of the parabola is (

p

2

,0) , since the circle touches directrix x = −

p

2

of the parabola,
the radius of the circle =

p

2

+

p

2

= p
Ρ equation of the circle is (x+

p

2

)2 + y2 = p2
⇒ x2+y2 - px -

3p2

4

= 0
this circle meets the parabola y2 = 2px at points whose abscissae are given by
x2 + 2px - px -

3p2

4

= 0
p x =

p

2

, x = −

3p

4

But x = −

3p

4

is not possible on parabola y2 = 2px