JEE Main 2020 — Parabola Question with Solution
From: JEE Main 2020 (Online) 6th September Morning Slot
Question
Let L1
be a tangent to the parabola y2 = 4(x + 1)
and L2 be a tangent to the parabola y2 = 8(x + 2)
such that L1 and L2 intersect at right angles. Then L1 and L2 meet on the straight line :
and L2 be a tangent to the parabola y2 = 8(x + 2)
such that L1 and L2 intersect at right angles. Then L1 and L2 meet on the straight line :
Choose an option
Show full solutionCorrect option: A
Correct answer
Ax + 3 = 0
Step-by-step explanation
L1 : y2 = 4(x + 1)
Equation of tangent y = m(x + 1) + ...(1)
L2 : y2 = 8(x + 2)
Equation of tangent y = m'(x + 2) +
y = m'x + 2 ....(2)
Since lines intersect at right angles
mm' = -1
m' =
Putting it in equation (2)
y =
y = ....(3)
From equation (1) and (3)
m(x + 1) + =
= 0
x + 3 = 0
Equation of tangent y = m(x + 1) + ...(1)
L2 : y2 = 8(x + 2)
Equation of tangent y = m'(x + 2) +
y = m'x + 2 ....(2)
Since lines intersect at right angles
mm' = -1
m' =
Putting it in equation (2)
y =
y = ....(3)
From equation (1) and (3)
m(x + 1) + =
= 0
x + 3 = 0
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This is a previous-year question from JEE Main 2020, 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.