Question

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

• A. $\frac{\pi }{2}$
• B. $\frac{\pi }{3}$
• C. $\frac{\pi }{6}$
• D. $\frac{\pi }{4}$

Answer 1

The correct option is A $\frac{\pi }{2}$

Given equation of parabola is
$y=x^2-5x+6$
$\frac{dy}{dx}=2x-5$
Slope of tangent at $(2,0)=m_1=4-5=-1$
Slope of tangent at $(3,0)=m_2=6-5=1$
$\Rightarrow m_1{m}_2=-1$
$\Rightarrow$ Angle between tangents $=\frac{\pi }{2}$