Published by:
CGP EDU Academic Team
Published on: August 13, 2026
Let a circle tangent to the directrix of a parabola 
has its centre coinciding with the focus of the parabola. Then the point of intersection of the parabola and circle is
A
( a , – a )
B
C
D
Text Solution
Verified by ExpertsThe correct answer is:
C
Given parabola is 
∴ ∴ Focus ( a /2, 0) and directrix is given by 
,
as circle touches the directrix.
∴ ∴ Radius of circle = distance from the point ( a /2, 0) to the line
∴ ∴ Equation of circle be 
…..(i)
also 
…..(ii)
Solving (i) and (ii) we get 
Putting these values in 
we get
and 
gives imaginary values of y .
∴ ∴ Required points are 
.
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