JEE Main 2020 — Application Of Derivatives Question with Solution
From: JEE Main 2020 (Online) 5th September Evening Slot
Question
If the lines x + y = a and x – y = b touch the
curve y = x2 – 3x + 2 at the points where the curve intersects the x-axis, then is equal to _______.
curve y = x2 – 3x + 2 at the points where the curve intersects the x-axis, then is equal to _______.
Enter your answer
Show full solutionCorrect answer: 0.5
Correct answer
0.5
Step-by-step explanation
y = x2
– 3x + 2
y = (x – 1)(x – 2)
At x-axis y = 0
x = 1, 2
So this curve intersects the x-axis at A(1, 0) and B(2, 0).
and
Equation of tangent at A(1, 0) :
y = –1(x –1)
x + y = 1
and equation of tangent at B(2, 0):
y = 1(x – 2)
x – y = 2
So a = 1 and b = 2
= 0.5
y = (x – 1)(x – 2)
At x-axis y = 0
x = 1, 2
So this curve intersects the x-axis at A(1, 0) and B(2, 0).
and
Equation of tangent at A(1, 0) :
y = –1(x –1)
x + y = 1
and equation of tangent at B(2, 0):
y = 1(x – 2)
x – y = 2
So a = 1 and b = 2
= 0.5
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