JEE Main 2020 — Application Of Derivatives Question with Solution
From: JEE Main 2020 (Online) 8th January Morning Slot
Question
Let the normal at a point P on the curve
y2 – 3x2 + y + 10 = 0 intersect the y-axis at .
If m is the slope of the tangent at P to the curve, then |m| is equal to
y2 – 3x2 + y + 10 = 0 intersect the y-axis at .
If m is the slope of the tangent at P to the curve, then |m| is equal to
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Show full solutionCorrect answer: 4
Correct answer
4
Step-by-step explanation
Given curve : y2
– 3x2
+ y + 10 = 0
2y - 6x + = 0
=
Let P be (x1, y1)
Slope of tangent at P =
Slope of normal at P =
Equation of normal (y – y1) = (x – x1)
This normal passes through point .
( – y1) = (0 – x1)
y1 = 1
Put y1 = 1 in equation of curve , then we get x1 = 2
|m| = slope of tangent = = = 4
2y - 6x + = 0
=
Let P be (x1, y1)
Slope of tangent at P =
Slope of normal at P =
Equation of normal (y – y1) = (x – x1)
This normal passes through point .
( – y1) = (0 – x1)
y1 = 1
Put y1 = 1 in equation of curve , then we get x1 = 2
|m| = slope of tangent = = = 4
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This is a previous-year question from JEE Main 2020, covering the Application Of Derivatives 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.