Note: This is part 2nd of a 2 part question, split as 2 separate questions here.

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- If $y=f(x)$ then $\large\frac{dy}{dx}$$=f'(x)$ is the rate of change of $y$ w.r.t $x$
- $\large\frac{dy}{dx_{(x_1,y_1)}}$ is the slope of the tangent to the curve at the point $(x_1,y_1) $ on the curve. It is the slope of the curve at that point.
- The normal at a point $(x_1,y_1)$ on $y=f(x)$ is perpendicular to the tangent at $(x_1,y_1)$

Step 1:

Let $ (x_1,y_1)$ be the point at which the tangent is $||$ to the y-axis

Therefore $ \large\frac{dy}{dx_{(x_1,y_1)}}$$=m \to \infty$

Step 2:

Now $\large\frac{dy}{dx_{(x_1,y_1)}}=\large\frac{1-x_1}{y_1-2}$$ \qquad m \to \infty =>y_1-2=\infty$

=>$y=2$

Step 3:

Substituting $y_1=2$ we find $x_1$

$x_1^2+4-2x_1-8+1=0$

=>$x_1^2-2x_1-3=0$

=>$ (x_1-3)(x_1+1)=0$

=>$x_1=3,-1$

Step 4:

The points are $ (3,2),(-1,2)$

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