Published by:
CGP EDU Academic Team
Published on: August 14, 2026
Let C 1 and C 2 be, respectively, the parabolas x 2 = y – 1 and y 2 = x – 1. Let P be any point on C 1 and Q be any point on C 2 . Let P 1 and Q 1 be the reflections of P and Q, respectively, with respect to the line y = x. Prove that P 1 lies on C 2 , Q 1 lies on C 1 and PQ > min {PP 1 , QQ 1 }. Hence or otherwise determine points P 0 and Q 0 on the parabola C1 and C2 respectively such that P 0 Q 0 ≤ PQ for all pairs (P, Q) with P on C 1 and Q on C 2 .
Text Solution
Verified by ExpertsThe correct answer is:
CHECK THE SOLUTION.
Sol. P0 = (1/2, 5/4), Q0 = (5/4, 1/2)
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