JEE Main 2018 — Parabola Question with Solution
JEE Main 2018 (15 Apr Shift 1 Online)
Question
Two parabolas with a common vertex and with axes along -axis and -axis, respectively, intersect each other in the first quadrant. if the length of the latus rectum of each parabola is 3 , then the equation of the common tangent to the two parabolas is?
Choose an option
Show full solutionCorrect option: C
Correct answer
C
Step-by-step explanation
As origin is the only common point to axis and -axis, so, origin is the common vertex Let the equation of two of parabolas be and
Now latus rectum of both parabolas
Two parabolas are and Suppose is the common tangent.
As, the tangent touches at one point only
So,
Form (i) and ( ii)
Hence,
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This is a previous-year question from JEE Main 2018, covering the Parabola chapter of Mathematics. PrepSharp catalogues every PYQ from JEE Main with a verified answer key and step-by-step solution prepared by IIT alumni — so you can search by chapter, topic or year and revise efficiently.