If the line $y=x$ is a tangent to the parabola $y=a x^{2}+b x+c$ at the point $(1,1)$ and the curve passes through $(-1,0)$, then

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If the line $y=x$ is a tangent to the parabola $y=a x^{2}+b x+c$ at the point $(1,1)$ and the curve passes through $(-1,0)$, then

3 Answers

kritika · Answer 1 · 2021-12-26T19:25:24+0000

Ans: (C)
Hint : $\frac{d y}{d x}=2 a x+b$
$$
\text { at }(1,1) \frac{d y}{d x}=2 a+b=1
$$
Now $(1,1)$ and $(-1,0)$ satisfies the curve
$$
\begin{aligned}
&a-b+c=0 \\
&a+b+c=1
\end{aligned}
$$
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$$
\mathrm{b}=\frac{1}{2} ; \mathrm{a}=\frac{1}{4} ; \mathrm{c}=\frac{1}{4}
$$

If the line \(y=x\) is a tangent to the parabola \(y=a x^{2}+b x+c\) at the point \((1,1)\) and the curve passes through \((-1,0)\), then

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