Q106 / 160 · AP EAMCET 2024 (22 May Shift 1) · Mathematics
Equation of the normal to the curve $y=x^2+x$ at the point $(1,2)$ is
- A$x-3 y+5=0$
- B$x+3 y+7=0$
- C$x+3 y+5=0$
- Correct answerD$x+3 y-7=0$
Solution
$y=x^2+x \Rightarrow \frac{d y}{d x}=2 x+\left.1 \Rightarrow \frac{d y}{d x}\right|_{(1,2)}=3$
Equation of normal at $(1,2)$ is $\begin{aligned} & y-2=\frac{-1}{\left(\frac{d y}{d x}\right)_{(1,2)}}(x-1) \\ & \Rightarrow y-2=\frac{-1}{3}(x-1) \Rightarrow x+3 y-7=0 \end{aligned}$
Equation of normal at $(1,2)$ is $\begin{aligned} & y-2=\frac{-1}{\left(\frac{d y}{d x}\right)_{(1,2)}}(x-1) \\ & \Rightarrow y-2=\frac{-1}{3}(x-1) \Rightarrow x+3 y-7=0 \end{aligned}$
Hence, the correct answer is option: 'D'.