Solve this following


If the curve $y=a x^{2}+b x+c, x \in R$, passes through the point $(1,2)$ and the tangent line to this curve at origin is $\mathrm{y}=\mathrm{x}$, then the possible values of $\mathrm{a}, \mathrm{b}, \mathrm{c}$ are :


  1. $\mathrm{a}=\frac{1}{2}, \mathrm{~b}=\frac{1}{2}, \mathrm{c}=1$

  2. $a=1, b=0, c=1$

  3. $a=1, b=1, c=0$

  4. $a=-1, b=1, c=1$

Correct Option: 3,


$a+b+c=2$   ................(2)

and $\left.\frac{\mathrm{dy}}{\mathrm{dx}}\right|_{(0,0)}=1$

$2 \mathrm{ax}+\left.\mathrm{b}\right|_{(0,0)}=1$


Curve passes through origin

So, $\mathrm{c}=0$

and $a=1$


Leave a comment


Click here to get exam-ready with eSaral

For making your preparation journey smoother of JEE, NEET and Class 8 to 10, grab our app now.

Download Now