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

Calculate the equation of the normal to the curve $y=x^2+2x+1$ at the point where the tangent is $y=4x+3$.

Find the equation of the normal to the curve $y=x^2-4x+7$ at $x=2$.

Find the equation of the normal to $y=3x^3-x^2+2$ at $x=-1$.

For the curve $y=3x^3-x$, find the equations of the normals at the points where the tangent is horizontal.

Find the equation of the normal to $y=4x^4-8x^2+5$ at $x=1$.

Find the equation of the normal to the curve $y=x^4-2x+1$ at $x=1$.

The tangent to the curve $y=2x^3+x^2-4x+1$ is $y=7x-3$. Find the equations of the normals at the point(s) of contact.

Find the equation of the normal to the curve $y=x^5-5x+4$ at $x=2$.

The tangent to $y=x^3-3x+2$ is $y=9x-7$. Find the equations of the normals at those points.

The normal to $y=x^2+kx+3$ at $x=3$ has slope $-\tfrac14$. Find $k$ and write the equation of this normal.

For the curve $y=\frac1x$, the tangent at some point is $y=-x+4$. Find the equation(s) of the normal.

The normal to $y=x^3-ax^2+bx-1$ at $x=1$ is $y=x+2$. Find $a$ and $b$.