Question Type 2: Calculating the normal to the curve at the point where tangent is known Bootcamps

Find the equation of the normal to the curve $y=\ln(x)$ at $x=4$.

For the curve $y=\frac{1}{x}$, the tangent at $x=-1$ has slope $m$. Determine the equation of the normal at that point.

Find the equation of the normal to the curve $y=\tfrac{x}{x-1}$ at $x=2$.

Find the equation of the normal to the curve $y = x^3 - 3x + 2$ at the point where the tangent has slope 6.

Calculate the equation of the normal to the curve $y = e^{2x} + x$ at the point where the tangent has slope 5.

Determine the equation of the normal to the curve $y=\arctan(x)$ at $x=1$.

Calculate the equation of the normal to the curve $y^2=4x+8y$ at the point $(0,0)$.

Find the equation of the normal to the curve defined by $x^2+xy+y^2=7$ at the point $(1,2)$.

The curve is $y=\sin x+x$. Find the equation of the normal at the point where its tangent has slope 1.

Find the equation of the normal to the curve $x^3+y^3=6xy$ at the point $(3,3)$.