Mathematics (AS)·Coordinate geometry · NSSCAS 1.4.1
Curves, lines & tangency
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Ever wondered how algebra can SEE a picture? In this lesson you will learn that a point lies on a curve exactly when its coordinates satisfy the equation. You will find where a line meets a curve by solving the equations together, and you will use the discriminant to tell whether a line crosses, touches or misses a curve. By the end you will find tangents like an examiner's dream candidate.
What you'll learn in this lesson
By the end you should be able to (NSSCAS Mathematics (AS) 1.4.1):
- Interpret the relationship between a graph and its equation: a point lies on a curve exactly when its coordinates satisfy the equation.
- Find the points of intersection of a line and a curve by solving their equations simultaneously.
- Use the discriminant of the resulting quadratic to decide whether a line crosses (two roots), touches (repeated root — a tangent) or misses (no real roots) a curve.
- Find an unknown constant so that a line is a tangent to a curve, and find the point of contact.
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