How do you find the equation of a line at a given point that is tangent to a circle?

  • Google+ icon
  • LinkedIn icon
  • 792 views

This question may start by giving you an equation, which you need to write in the form of the standard equation of a circle (usually by completing the square). This allows you to see the centre of the circle. As you now have two coordinates you can work out the gradient of the line between the centre of the circle and the given point on the circumference. As this line is perpendicular to the tangent on the circle, the gradient is the negative reciprocal. Now you know the gradient of the tangent and a point it crosses through, you can find the equation of the line by substituting these values into the standard equation of a line y=mx+c

Tom W. A Level Maths tutor, GCSE Maths tutor, GCSE Physics tutor

About the author

is an online A Level Maths tutor with MyTutor studying at Durham University

Still stuck? Get one-to-one help from a personally interviewed subject specialist.

95% of our customers rate us

Browse tutors

We use cookies to improve your site experience. By continuing to use this website, we'll assume that you're OK with this. Dismiss

mtw:mercury1:status:ok