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CGP EDU Academic Team
Published on: August 14, 2026
If the parabola y = f(x), having axis parallel to y-axis, touches the line y = x at (1, 1) then
Text Solution
Verified by ExpertsThe correct answer is:
B
Let f(x) = ax 2 + bx + c
⇒ f ′ (x) = 2ax + b
Thus, f(0) = C and f ′ (0) = b
We have that information that y = f(x) is being touched by y = x at (1, 1)
⇒ ax 2 + bx + c = x
should have x = 1 at its repeated root.
⇒ ax 2 + x(b –1) + c = 0 are 1, 1
⇒ 
= 2, 
= 1
⇒ 1 – b = 2a = 2c
⇒ 1 – f ′ (0) = 2f(0)
or 2f (0) + f ′ (0) = 1
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