Tangent at a known point on the circle (NF)
A standard method from Equations of circles: the steps and worked examples.
Steps
- Slope of the radius from the centre to the point.
- Tangent slope = −1 ÷ radius slope (tangent ⊥ radius).
- Point-slope form.
Worked examples
Example 1: Tangent at a known point on the circle (NF): find the tangent to x² + y² − 6x + 4y − 12 = 0 at (6, 2).
centre (3, −2); slope of radius = (2 + 2)/(6 − 3) = 4/3
tangent slope = −3/4
y − 2 = −¾(x − 6)
3x + 4y − 26 = 0For the whole topic, read Equations of circles: key points, common mistakes and how the DSE tests it.