The point on the curve y = (x - 1)(x - 2) at which the tangent makes an angle of 135° with the positive direction of x-axis has coordinates
Answer & explanation
Correct answer: option 1
Let $\left(x_1, y_1\right)$ be the required point. Then,
$\left(\frac{d y}{d x}\right)_{\left(x_1, y_1\right)}=\tan 135^{\circ}$
$\Rightarrow 2 x_1-3=-1$ $\left[∵ y=(x-1)(x-2) \Rightarrow \frac{d y}{d x}=2 x-3\right]$
$\Rightarrow x_1=1$
Since $\left(x_1, y_1\right)$ lies on $y=(x-1)(x-2)$
∴ $y_1=\left(x_1,-1\right)\left(x_1-1\right)=(1-1)(1-2)=0$
Hence, (1, 0) is the required point.