Last updated: October 22, 2026 · Written by the Math Made Easy math teachers
Looking for a parabola focus directrix and tangent lines quiz? Then this Geometry quiz on Parabolas from Focus and Directrix, and Tangents asks 10 multiple-choice questions with instant feedback. Ten multiple-choice questions on parabola definitions, focus and directrix, and tangent properties. Each explanation points out the slip behind the tempting wrong choices.
Standards: G-GPE.A.2, G-C.A.4 · Level: Grade 10 Geometry
What this Parabolas from Focus and Directrix, and Tangents quiz checks
- Parabola: distance to the focus equals distance to the directrix.
- Opening up or down: (x − h)² = 4p(y − k), focus (h, k + p), directrix y = k − p.
- Opening right or left: (y − k)² = 4p(x − h), focus (h + p, k), directrix x = h − p.
- Two tangent segments from an outside point are congruent, and PT² = OP² − r².
The 10 questions of the quiz
- Which description defines a parabola?
- What is the focus of x² = 8y?
- What is the directrix of x² = 8y?
- The parabola y² = −20x opens
- How far is P from the directrix?
- A parabola has vertex (−3, 5) and focus (−3, 9). What is p?
- Two tangent segments from one point to a circle have lengths 3x + 8 and 5x − 4. What is x?
- What is PT?
- A tangent line to a circle is always
- In the construction of a tangent from P, which circle has diameter OP?
After the quiz
Missed a question? Reread the Parabolas from Focus and Directrix, and Tangents lesson, then take the quiz again. Next, solve the Geometry worksheet on Parabolas from Focus and Directrix, and Tangents, one star first, then two and three stars. Finally, take the chapter test under real conditions, without notes and with a timer.