When will a line intersect a circle

Resources on this page:
Video going through an SBD question | Key points | SBD with worked solution | Interactive used in the video

Pure 1 Ex 6D Q10 - the answer is at the bottom of this page

Remember: productive practice is perfect preparation

Once you have seen and understood how to do the question then do it yourself
If you used help then after a few days retry the question without help

Key Points

You need to be able to:

Substitute a linear expression into a quadratic expression containing x² and y²
Simplify a quadratic expression with an unknown coefficient
Find the discriminant of a quadratic with an unknown coefficient
Solve quadratic inequalities

Explore

You can download the interactive used in the video (Geogebra file)

The interactive allows you to investigate the values of p for which the circle and the line do not intersect. The interactive is editable, so you can change the line and the circle used.

Answer to the textbook question at the top of this page