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Equation of a Tangent (Edexcel GCSE Maths)
Revision Note
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 Gradients
- A TANGENT just touches a circle (but does not cross it)
- The gradient of the tangent at point P is PERPENDICULAR to the gradient of the radius OP
- remember, perpendicular gradients multiply to -1 (they are negative reciprocals)
- So if P is a point on the circumference, then the gradient of the radius OP is .
- Therefore the gradient of the tangent to the circle at P is
- From here, use to find the equation of the tangent
Examiner Tip
- 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
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