Equation of a normal

CalculusCourse skill

Find the line perpendicular to the tangent at a point.

Find the point and tangent gradient .
For , the normal gradient is .
Use .

Example 1

Find an equation of the normal to the curve at .

Find the gradient function.

Substitute the stated value of

Find the point on the curve.

Take the negative reciprocal of the tangent gradient.

Use the point-gradient form.

Example 2

Find an equation of the normal to the curve at .

Find the gradient function.

Substitute the stated value of

Find the point on the curve.

Take the negative reciprocal of the tangent gradient.

Use the point-gradient form.

Remember
All questions here have a non-zero tangent gradient. A horizontal tangent instead has the vertical normal .

Your turn

5 practice questions

Question 1

Find an equation of the normal to the curve at .

Check answer

Find the gradient function.

Substitute the stated value of

Find the point on the curve.

Take the negative reciprocal of the tangent gradient.

Use the point-gradient form.

Question 2

Find an equation of the normal to the curve at .

Check answer

Find the gradient function.

Substitute the stated value of

Find the point on the curve.

Take the negative reciprocal of the tangent gradient.

Use the point-gradient form.

Question 3

Find an equation of the normal to the curve at .

Check answer

Find the gradient function.

Substitute the stated value of

Find the point on the curve.

Take the negative reciprocal of the tangent gradient.

Use the point-gradient form.

Question 4

Find an equation of the normal to the curve at .

Check answer

Find the gradient function.

Substitute the stated value of

Find the point on the curve.

Take the negative reciprocal of the tangent gradient.

Use the point-gradient form.

Question 5

Find an equation of the normal to the curve at .

Check answer

Find the gradient function.

Substitute the stated value of

Find the point on the curve.

Take the negative reciprocal of the tangent gradient.

Use the point-gradient form.

Example 1

Example 2

Your turn

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