Line and circle (NF)
A standard method from Equations of circles: the steps and worked examples.
Steps
- Make y (or x) the subject of the line.
- Substitute into the circle. You get a quadratic in x.
- Use Δ:
| Δ | The line… |
|---|---|
| > 0 | cuts the circle at 2 points |
| = 0 | is a tangent (1 point) |
| < 0 | misses the circle |
- To find the points, solve the quadratic and substitute back.
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.