Question

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 $y = x ,$ then the possible values of $a , b , c$ are :

• A. $a =\frac{1}{2}, b =\frac{1}{2}, c =1$
• B. $a =1, b =0, c =1$
• C. $a =1, b =1, c =0$
• D. $a=-1, b=1, c=1$

Answer 1

Answer: (C)

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

Answer 2

$a+b+c=2$...(1) and $\left.\frac{ dy }{ dx }\right|_{(0,0)}=1$ $2 ax +\left. b \right|_{(0,0)}=1$ $b =1$ Curve passes through origin So, $c=0$ and $a=1$