Question

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

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

Answer 1

Answer: (D)

$\pi /2$

Given equation $y=x^2-5x+6,$ given points

$(2,0),(3,0)$

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

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

$m_2={\left(\frac{dy}{dx}\right)}_{(3,0)}=6-5=1$

Since $m_1{m}_2=-1$

$\Rightarrow$ tangents are at right angle$=\frac{\pi }{2}$