Question

Angle between the tangents to the curve $y=x^2-5x+6$ at the points $(2,0)\&(3,0)$ is

• A. $\pi /2$
• B. $\pi /6$
• C. $\pi /4$
• D. $\pi /3$

Answer 1

The correct option is A

$\pi /2$

Explanation for the correct option:

Step1. Differentiating the equation with respect to $\text{'}x\text{'}$

Given equation of curve

$y=x^2-5x+6$

Differentiate with respect to ‘x’.

$\frac{\mathrm{dx}}{\mathrm{dy}}=2x-5$

Step2. Finding slope from given point.

slope of tangent to the curve at $\left(2,0\right)$ is

$\begin{array}{rcl}{\left(\frac{dx}{dy}\right)}_{(2,0)}& =& 2\left(2\right)-5\\ & =& 4-5\\ & =& -1\\ m_1& =& -1\end{array}$

slope of tangent to the curve at $\left(3,0\right)$ is

$\begin{array}{rcl}{\left(\frac{dx}{dy}\right)}_{\left(3,0\right)}& =& 2\left(3\right)-5\\ & =& 6-5\\ & =& 1\\ m2& =& 1\\ sincem1.m2& =& -1\times 1=-1\end{array}$

Therefore Angle between the tangents to the curve at $(2,0)\&(3,0)$ is $\frac{\mathrm{\pi }}{2}$

Hence, option $\left(A\right)$ is correct.