JEE PYQ: Application Of Derivatives Question 14
Question 14 - 2021 (24 Feb Shift 2)
If the curve $y = ax^2 + bx + c$, $x \in \mathbb{R}$, passes through the point $(1, 2)$ and the tangent line to this curve at origin is $y = x$, then the possible values of $a$, $b$, $c$ are:
(1) $a = 1, b = 1, c = 0$
(2) $a = -1, b = 1, c = 1$
(3) $a = 1, b = 0, c = 1$
(4) $a = \frac{1}{2}, b = \frac{1}{2}, c = 1$
Show Answer
Answer: (1)
Solution
Curve passes through origin: $c = 0$. Tangent at origin: $y’(0) = b = 1$. Through $(1,2)$: $a + 1 + 0 = 2 \Rightarrow a = 1$.
BETA
