The angle between the tangents to the curve y=x2-5x+6 at points (.2,0.) and (.3,0.) is

Question

The angle between the tangents to the curve y=x2-5x+6 at points (.2,0.) and (.3,0.) is (A) (π /6) (B) (π /4) (C) (π /3) (D) (π /2)

Tardigrade Admin · Accepted Answer

We have, y=x2-5x+6 ⇒ (d y/d x)=2x-5 ∴ m1=((d y/d x))(2 , 0)=2⋅ 2-5=-1 ∴ m2=((d y/d x))(3 , 0)=2⋅ 3-5=1 Since, m1⋅ m2=-1 , hence angle between two tangents is (π /2) .

Q. The angle between the tangents to the curve $y = x^{2} - 5 x + 6$ at points $(2, 0)$ and $(3, 0)$ is

$\frac{π}{6}$

$\frac{π}{4}$

$\frac{π}{3}$

$\frac{π}{2}$

We have,
$y = x^{2} - 5 x + 6$
$\Rightarrow \frac{d y}{d x} = 2 x - 5$
$∴ m_{1} = (\frac{d y}{d x})_{(2, 0)} = 2 \cdot 2 - 5 = - 1$
$∴ m_{2} = (\frac{d y}{d x})_{(3, 0)} = 2 \cdot 3 - 5 = 1$
Since, $m_{1} \cdot m_{2} = - 1$ , hence angle between two tangents is $\frac{π}{2}$ .

Q. The angle between the tangents to the curve y=x2−5x+6 at points (2,0) and (3,0) is

6π​

4π​

3π​

2π​