JEE Main 2021 — Definite Integration Question with Solution
From: JEE Main 2021 (Online) 16th March Morning Shift
Question
If the normal to the curve y(x) = at a point (a, b) is parallel to the line x + 3y = 5, a > 1, then the value of | a + 6b | is equal to ___________.
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Show full solutionCorrect answer: 406
Correct answer
406
Step-by-step explanation
Normal to the curve at point P(a, b) is parallel to the line x + 3y = 5.
mnormal =
mtangent = 3 =
Given y(x) =
y'(x) = (2x2 15x + 10)
at point P(a, b)
3 = (2a2 15a + 10)
2a2 15a + 7 = 0
2a2 14a a + 7 = 0
2a(a 7) 1 (a 7) = 0
a = or 7,
given a > 1 a = 7
As P(a, b) lies on curve
mnormal =
mtangent = 3 =
Given y(x) =
y'(x) = (2x2 15x + 10)
at point P(a, b)
3 = (2a2 15a + 10)
2a2 15a + 7 = 0
2a2 14a a + 7 = 0
2a(a 7) 1 (a 7) = 0
a = or 7,
given a > 1 a = 7
As P(a, b) lies on curve
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