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Q. The angle between the tangents to the curve $y=x^{2}-5x+6$ at points $\left(\right.2,0\left.\right)$ and $\left(\right.3,0\left.\right)$ is

NTA AbhyasNTA Abhyas 2022

Solution:

We have,
$y=x^{2}-5x+6$
$\Rightarrow \frac{d y}{d x}=2x-5$
$\therefore m_{1}=\left(\frac{d y}{d x}\right)_{\left(2 , 0\right)}=2\cdot 2-5=-1$
$\therefore m_{2}=\left(\frac{d y}{d x}\right)_{\left(3 , 0\right)}=2\cdot 3-5=1$
Since, $m_{1}\cdot m_{2}=-1$ , hence angle between two tangents is $\frac{\pi }{2}$ .