Tangency
SAT glossary · Course Foundations
Definition
Touching at exactly one point, which the test always encodes as Δ = 0 on the combined equation. Every "tangent to," "touches at exactly one point," "intersects exactly once," or "has a double root" item is Δ=0; "does not intersect" is Δ<0; "intersects twice" is Δ>0. Recognizing the vocabulary that invokes the discriminant is most of the skill.
Tangency in plain English
Tangency means two shapes (like a line and a curve, or two curves) touch at exactly ONE single point and don't cross through each other. On this test, tangency always gets translated into one specific math fact: when you combine the two equations into one and calculate its discriminant (Δ=b^2-4ac), tangency corresponds to Δ=0 exactly. Any phrase like 'tangent to,' 'touches at exactly one point,' 'intersects exactly once,' or 'has a double root' is all secretly asking you to set the discriminant equal to zero. Meanwhile, Δ<0 means the shapes never touch at all, and Δ>0 means they cross at two separate points. Learning to recognize this specific vocabulary is really most of what this skill requires.
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