Intersection of a Line and a Curve

Substitute the line equation into the curve equation and collect all terms on one side. ax2+bx+c=0 D=b2-4ac Cuts at two distinct points: b2-4ac>0 Touches: the line is a tangent, b2-4ac=0 Does not intersect: b2-4ac<0 Intersections **The question says** | **Condition to use** The line cuts or intersects the curve at two distinct points | b2-4ac>0 The line touches the curve; the line is a tangent | b2-4ac=0 The line meets the curve (one or two points) | b2-4ac >= 0 The line does not intersect the curve | b2-4ac<0 Use the coefficients of the equation obtained after substitution. Find each y-coordinate from the line equation.