Question

Angle between the tangents 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

Answer: (A)

$\frac{\pi }{2}$

Given equation of curve $y=x^2-5x+6$

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

Slope of tangent to the curve at $(2,0)$ is

${\left(\frac{dy}{dx}\right)}_{(2,0)}=2\left(2\right)-5=-1=m_1$

Slope of tangent to the curve at $(3,0)$ is

${\left(\frac{dy}{dx}\right)}_{(3,0)}=2\left(3\right)-5=1=m_2$

Since $m_1{m}_2=-1$

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