Geometry Equations of Circles and Parabolas Test with Point Values (PDF)

Geometry math test: Equations of Circles and Parabolas – Maths PDF

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This circle equations test for Geometry covers equations of circles and parabolas (Common Core G-GPE.A.1, G-GPE.A.2), with a free PDF to print.

This 45-minute test checks equations of circles and parabolas. It has 9 questions worth 20 points in total. Show every step of the work, label diagrams, and include units where they apply. Calculators are allowed unless the teacher says otherwise.

Time and points

About this test

Grade: Geometry
Chapter: Equations of Circles and Parabolas
Standards: G-GPE.A.1, G-GPE.A.2
Time: 45 minutes
Total: 20 points

Circle equations test: questions

Question 1 – Write an equation [2 pts]

Write the equation of the circle with center (-3, 4) and radius 6.

Question 2 – Center and radius [2 pts]

Find the center and radius of the circle \((x + 7)^{2} + (y – 4)^{2} = 64\).

Question 3 – Complete the square [3 pts]

Rewrite \(x^{2} + y^{2} + 6x – 10y + 18 = 0\) in center-radius form. (1 point)
State the center. (1 point)
State the radius. (1 point)

Question 4 – Point and circle [2 pts]

Circle with center C.

Circle C has equation \((x – 1)^{2} + (y – 2)^{2} = 25\). Decide whether (2, 3), (4, 6) and (7, 3) are inside, on, or outside it.

Question 5 – Circle from a diameter [2 pts]

AB is a diameter.

The endpoints of a diameter of a circle are (-1, 2) and (7, 8). Write the equation of the circle.

Question 6 – Line meets circle [2 pts]

Find the points where the line y = 2x meets the circle x² + y² = 20.

Question 7 – Parabola [3 pts]

Parabola with focus and directrix.

A parabola has focus (0, 2) and directrix y = -2. (a) Write its equation. (b) Show that (4, 2) is on it. (c) Find the distance from (4, 2) to the directrix.

Question 8 – Tangent circle [2 pts]

A circle has center (5, -4) and is tangent to the y-axis. Write its equation.

Question 9 – Fire tower [2 pts]

A fire tower at (0, 0) can see 15 miles in every direction. Is a fire at (9, 12) visible? Is a fire at (12, 10)?

Key facts behind this circle equations test

Key facts

Circle: (x – h)^2 + (y – k)^2 = r^2, center (h, k), radius r.
Read the center with opposite signs from the equation.
Inside, on, or outside: compare (x – h)^2 + (y – k)^2 with r^2.
Complete the square to convert x^2 + y^2 + Dx + Ey + F = 0.
Parabola with focus (0, p) and directrix y = -p: x^2 = 4py.

How to use this circle equations test

Time yourself: the test is designed for an average student in 45 minutes. Answer the questions you are sure of first, then come back to the longer ones and check your units.

All Geometry chapters: Geometry math.

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