Published by:
CGP EDU Academic Team
Published on: August 14, 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 
.
Prepare Smarter with CGP Edu
Get practice questions, solutions, and test series in one place.
Write a Review
Share your experience with this question and solution.
Commentary
Send your comment, doubt, correction, or feedback to admin.
Similar Questions
Explore conceptually related problems
If a double ordinate of the parabola be of length , then the angle between the lines joining the …
PQ is a double ordinate of the parabola . The locus of the points of trisection of PQ is
If the vertex of a parabola be at origin and directrix be , then its latus rectum is
The latus rectum of a parabola whose directrix is and focus is (3, – 4), is
The points on the parabola whose ordinate is three times the abscissa are
The points on the parabola whose focal distance is 4, are