Q. Angle between the tangents to the curve $y = x^{2} - 5x + 6$ at the point (2, 0) and (3, 0) is
A) $\frac{\pi}{2}$
B) $\frac{\pi}{6}$
C) $\frac{\pi}{4}$
D) $\frac{\pi}{3}$
Explanation
(a)
Since, $y = x^{2} - 5x + 6$
$\therefore\ \ \ \ \ \ \frac{dy}{dx} = 2x - 5$
Now, $m_{1} = \left( \frac{dy}{dx} \right)_{(2,\ 0)} = 4 - 5 = - 1$
And $m_{2} = \left( \frac{dy}{dx} \right)_{(3,\ 0)} = 6 - 5 = 1$
Now, $m_{1}m_{2} = - 1 \times 1 = - 1$
Hence, angle between the tangents is $\frac{\pi}{2}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.