JEE Main 2021 (Online) 24th February Evening ShiftQuestion 1
If the curve $y=ax^{2}+bx+c$, $x\in\mathbf{R}$, 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 :
Differentiation and its Application
Solution
Concept. The tangent at the origin is $y=x$: the curve passes through $O$ with slope $1$. Formulas used. (1) $y'=2ax+b$Step 1 - Through $O$. $c=0$. Step 2 - Slope at $O$. By (1), $b=1$. Step 3 - Through $(1,2)$. $a+b=2$, so $a=1$. Answer: (A)