Published by:
CGP EDU Academic Team
Published on: August 14, 2026
The locus of the point of intersection of two normals to the parabola 
which are at right angles to each other, is
A
B
C
D
None of these
Text Solution
Verified by ExpertsThe correct answer is:
A
Given parabola is 
.....(i)
Let 
and 
be two points on the parabola (i)
Normal at P , Q are 
......(ii) and
......(iii)
(ii)–(iii) gives 
,
∴ ∴ 
.....(iv)
From (ii), 
⇒ ⇒ 
.....(v)
Since normals (ii) and (iii) are at right angles, ∴ ∴ 
⇒ ⇒ 
∴ ∴ From (iv), 
and from (v) 
⇒ ⇒ y 
⇒ ⇒ y 
⇒ ⇒
⇒ ⇒ 
which is the required locus.
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