# If the curve $y = ax^{2}+bx+c,x\; \epsilon \; R,$ passes through the point $\left ( 1,2 \right )$ and the tangent line to this curve at origin is $y=x,$ then the possible values of a , b, c are : Option: 1 $a=\frac{1}{2},b=\frac{1}{2},c=1$ Option: 2 $a=-1,b=1,c=1$ Option: 3 $a=1,b=1,c=0$ Option: 4 $a=1,b=0,c=1$

$y=a x^{2}+b x+c$

\begin{aligned} &a+b+c=2\\ &\text { and }\left.\frac{\mathrm{dy}}{\mathrm{dx}}\right|_{(0,0)}=1\\ &2 \mathrm{ax}+\left.\mathrm{b}\right|_{(0,0)}=1 \end{aligned}

$\\\mathrm{b}=1\\\\\text{Curve passes through origin } \\\\\text{So, }c=0\text{ and } \mathrm{a}=1$

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