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Parabola Focus Directrix and Tangent Lines Test – Geometry Math (Printable PDF)

Last updated: October 22, 2026 · Written by the Math Made Easy math teachers

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Looking for a parabola focus directrix and tangent lines test? Then this Geometry test on Parabolas from Focus and Directrix, and Tangents checks the whole chapter, with points for each question. This test has 8 questions worth 20 points and is designed for 45 minutes. A calculator is allowed. Show the vertex and the value of p, and justify each tangent length with a right triangle.

Standards: G-GPE.A.2, G-C.A.4 · Level: Grade 10 Geometry

Time: 45 minutes · 8 questions · Total: 20 points · Calculator: as allowed by your teacher

Question 1 Equation from the Focus (2 points)

Write the equation of the parabola with focus (0, 10) and directrix y = −10.

Question 2 Parabola Opening Left or Right (3 points)

Write the equation of the parabola with focus (−3, 2) and directrix x = −7.

Question 3 Complete the Square (3 points)

Rewrite x² + 10x + 12y + 49 = 0 in vertex form and give the focus and directrix.

Question 4 Is the Point on the Parabola? (2 points)

−14−12−10−8−6−4−22468101214−7−5−3−11357911xyFVdirectrixP
Focus (0, 5), directrix y = −5.

Is P(10, 5) on the parabola? Compare distances to the focus and the directrix.

Question 5 Tangent Segment Length (2 points)

OPTS1237?
Not drawn to scale.

A circle has radius 12 and OP = 37. Find the length of the tangent segment PT.

Question 6 Tangent Segments with Algebra (3 points)

Tangent segments PA and PB to a circle of radius 12 have lengths PA = 4x − 9 and PB = 2x + 11. Find x, PA, and the distance OP from P to the center to the nearest tenth.

Question 7 Telescope Dish (3 points)

A dish has a parabolic cross-section with vertex at the origin opening up. It is 36 inches wide and 6 inches deep. How far above the vertex is the focus?

Question 8 Why the Construction Works (2 points)

In the construction of a tangent from an outside point P, a circle is drawn on diameter OP and meets circle O at T. Explain why PT is tangent to circle O.

View the Parabola Focus Directrix And Tangent Lines test answer key with scoring

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