Geometry Parabola Tangents Quiz – Free PDF

Contents

This geometry parabola tangents quiz asks 10 multiple-choice questions on parabolas from focus and directrix, and tangent lines to a circle, and each answer comes with a short explanation.

Ten multiple-choice questions check the definition of a parabola, equations from a focus and a directrix, and the main facts about tangent lines to circles and their constructions. Each question has exactly one correct answer.

GeometryCommon Core: G-GPE.A.2 · G-C.A.4

🎯 Parabolas from Focus and Directrix, and Tangent Lines to a Circle – Geometry math quiz

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Answered: 0 / 10

Question 1

Which statement defines a parabola?

A The sum of the distances to two fixed points is constant

B Every point is the same distance from one fixed center

C The difference of the distances to two fixed points is constant

D Every point is the same distance from the focus and from the directrix

Question 2

A parabola has focus \((5,0)\) and directrix \(x=-5\). Which equation describes it?

A \(y^{2}=10x\)

B \(x^{2}=20y\)

C \(y^{2}=-20x\)

D \(y^{2}=20x\)

Question 3

What is the focus of the parabola \(x^{2}=16y\)?

A \((0,4)\)

B \((0,16)\)

C \((0,8)\)

D \((4,0)\)

Question 4

What is the focus of the parabola \(y^{2}=-8x\)?

A \((2,0)\)

B \((-2,0)\)

C \((0,-2)\)

D \((-8,0)\)

Question 5

The parabola shown has vertex V(1, 2) and focus F(1, 4). What is the equation of its directrix?

Vertex V and focus F.

A \(y=2\)

B \(y=0\)

C \(y=6\)

D \(y=-2\)

Question 6

In the figure, \(\overline{PT}\) is tangent to the circle at T, \(OT=6\) and \(PT=8\). Find OP.

Tangent PT.

A 10

B 14

C 12

D \(2\sqrt{7}\)

Question 7

Tangent segments \(\overline{PA}\) and \(\overline{PB}\) have lengths \(5x-3\) and \(2x+9\). What is PA?

A 4

B 34

C 17

D 7

Question 8

In the construction of a tangent from P to the circle with center O, M is the midpoint of OP. What is the next step?

Construction in progress.

A Draw the circle centered at M through O; it meets the given circle at the tangent points

B Draw the circle centered at P through O; it meets the given circle at the tangent points

C Draw the line through M perpendicular to OP; it is the tangent line

D Draw the line through P parallel to the radius from O to M

Question 9

Tangents from P touch a circle with center O at A and B, and \(m\angle APB=62^{\circ}\). Find \(m\angle AOB\).

Angle APB = 62°.

A \(28^{\circ}\)

B \(128^{\circ}\)

C \(118^{\circ}\)

D \(90^{\circ}\)

Question 10

Segment PT is drawn from P to a point T on a circle with center O. Which lengths (OT, PT, OP) show that PT is tangent at T?

A 6, 8, 11

B 5, 10, 12

C 6, 8, 10

D 4, 5, 7

🎉 Quiz complete!

0 / 10

How does this quiz work?

Read each question, choose one answer among A, B, C and D, then check it: a short explanation appears after every answer. Your score out of 10 is shown at the end, and you can restart the quiz as often as you like.

What should you review before the quiz?

Reread the key facts of the lesson and the worked example. If a question is hard, go back to the matching part of the lesson, then try the quiz again. Write your work on scrap paper: most mistakes come from skipping a step, not from the idea itself.

Remember:

A parabola is the set of points equidistant from the focus and the directrix (G-GPE.A.2).
Vertex (h, k): (x – h)^2 = 4p(y – k) has focus (h, k + p) and directrix y = k – p; (y – k)^2 = 4p(x – h) opens sideways.
p is the signed distance from the vertex to the focus; a negative p means the parabola opens down or left.
A tangent to a circle is perpendicular to the radius at the point of tangency (G-C.A.4).
Tangent segments from one outside point are congruent; the circle on diameter OP gives the tangent points in a construction.