Substitute the line equation into the curve equation and collect all terms on one side.
\(ax^2+bx+c=0\qquad D=b^2-4ac\)
Cuts at two distinct points: \(b^2-4ac>0\)
Touches: the line is a tangent, \(b^2-4ac=0\)
Does not intersect: \(b^2-4ac<0\)
Intersections
| The question says | Condition to use |
|---|---|
| The line cuts or intersects the curve at two distinct points | |
| The line touches the curve; the line is a tangent | |
| The line meets the curve (one or two points) | |
| The line does not intersect the curve |
Use the coefficients of the equation obtained after substitution. Find each \(y\)-coordinate from the line equation.
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