Revision NotesExam QuestionsFlashcardsPast Papers
GCSEMathsEdexcelHigherRevision Notes2. AlgebraEquation of a CircleEquation of a Tangent

Equation of a Tangent (Edexcel GCSE Maths)

Revision Note

Amber

Author

Amber

Last updated

Did this video help you?

Equation of a Tangent

How do we find the equation of a tangent to a circle?

  • First, make sure you are familiar with equations of straight lines and perpendicular lines

  • A tangent just touches a circle (but does not cross it)

  • The tangent at point P is perpendicular to the radius OP

    • remember, the gradients of perpendicular lines multiply to -1

      • they are negative reciprocals

  • So if P is a point open parentheses a comma space b close parentheses on the circumference, then the gradient of the radius OP is fraction numerator b minus 0 over denominator a minus 0 end fraction equals b over a.

    • Therefore the gradient of the tangent to the circle at P is negative a over b

  • From here, use bold italic y bold equals bold italic m bold italic x bold plus bold italic c to find the equation of the tangent

Examiner Tips and Tricks

  • Solving simultaneous equations of circle and tangent only gives one solution

    • so if you are asked to show a line is a tangent, solve the simultaneous equations and show there is only one solution

  • Always draw a diagram to help!

Worked Example

The graph shows the circle with the equation x squared plus y squared equals 100.

Circle Radius Tangent (before)

Find an equation of the tangent to the circle at the point P open parentheses 8 comma space 6 close parentheses.

Find the gradient of the radius by finding te gradient of the line segment form the origin to the point P

Gradient space of space O P equals fraction numerator 6 minus 0 over denominator 8 minus 0 end fraction equals 6 over 8 equals 3 over 4

Find the gradient of the tangent by taking the negative reciprocal of the gradient of the radius

m equals negative 4 over 3

Substitute m equals negative 4 over 3, x equals 8 and y equals 6 into y equals m x plus c to find the value of c

6 equals negative 4 over 3 cross times 8 plus c 6 equals negative 32 over 3 plus c c equals 6 plus 32 over 3 c equals 50 over 3

The equation of the tangent is y equals negative 4 over 3 x plus 50 over 3

You've read 0 of your 5 free revision notes this week

Sign up now. It’s free!

Join the 100,000+ Students that ❤️ Save My Exams

the (exam) results speak for themselves:

    Test yourselfFlashcards

    Did this page help you?

    Previous:Equation of a CircleNext:Finding Gradients of Tangents
    Amber

    Author: Amber

    Expertise: Maths

    Amber gained a first class degree in Mathematics & Meteorology from the University of Reading before training to become a teacher. She is passionate about teaching, having spent 8 years teaching GCSE and A Level Mathematics both in the UK and internationally. Amber loves creating bright and informative resources to help students reach their potential.