Geometry Equation Circle Quiz – Free PDF

Contents

This geometry equation circle quiz asks 10 multiple-choice questions on equation of a circle, and each answer comes with a short explanation.

Ten multiple-choice questions check the standard form of a circle, center and radius, completing the square, and points inside, on or outside a circle. Choose one answer for each, then read the explanation to catch common sign and squaring mistakes.

GeometryCommon Core: G-GPE.A.1

🎯 Equation of a Circle – Geometry math quiz

Score: 0 / 10

Answered: 0 / 10

Question 1

A circle centered at a lattice point.

What is the center of the circle shown?

A \((-2,3)\)

B \((2,3)\)

C \((2,-3)\)

D \((-3,2)\)

Question 2

Which equation describes the circle with center \((1,-4)\) and radius 3?

A \((x-1)^{2}+(y+4)^{2}=9\)

B \((x+1)^{2}+(y-4)^{2}=9\)

C \((x-1)^{2}+(y+4)^{2}=3\)

D \((x-1)^{2}+(y-4)^{2}=9\)

Question 3

What is the radius of the circle \((x-2)^{2}+(y+6)^{2}=49\)?

A \(49\)

B \(\sqrt{7}\)

C \(14\)

D \(7\)

Question 4

The circle x² + y² = 25.

The circle \(x^{2}+y^{2}=25\) is shown. Which point lies outside the circle?

A \((3,-4)\)

B \((0,-5)\)

C \((-2,4)\)

D \((4,4)\)

Question 5

What is \(x^{2}+y^{2}-8x+2y-8=0\) in standard form?

A \((x+4)^{2}+(y-1)^{2}=25\)

B \((x-4)^{2}+(y+1)^{2}=9\)

C \((x-4)^{2}+(y+1)^{2}=25\)

D \((x-4)^{2}+(y+1)^{2}=8\)

Question 6

What are the center and radius of the circle \(x^{2}+y^{2}+6x-4y-3=0\)?

A \((3,-2)\), radius 4

B \((-3,2)\), radius 4

C \((-3,2)\), radius 16

D \((-6,4)\), radius 4

Question 7

A circle with a horizontal radius.

Which equation matches the graph?

A \((x-1)^{2}+(y+2)^{2}=9\)

B \((x+1)^{2}+(y-2)^{2}=3\)

C \((x+1)^{2}+(y+2)^{2}=9\)

D \((x+1)^{2}+(y-2)^{2}=9\)

Question 8

A circle has a diameter with endpoints \((0,0)\) and \((8,6)\). What is its equation?

A \((x-4)^{2}+(y-3)^{2}=100\)

B \((x-8)^{2}+(y-6)^{2}=25\)

C \((x-4)^{2}+(y-3)^{2}=25\)

D \((x-4)^{2}+(y-3)^{2}=5\)

Question 9

Where is the point \((-3,-1)\) relative to the circle \((x+6)^{2}+(y-3)^{2}=25\)?

A It is inside the circle

B It is on the circle

C It is outside the circle

D It is the center of the circle

Question 10

A circle with center \((3,4)\) is tangent to the x-axis. What is its equation?

A \((x-3)^{2}+(y-4)^{2}=16\)

B \((x-3)^{2}+(y-4)^{2}=9\)

C \((x-3)^{2}+(y-4)^{2}=25\)

D \((x-3)^{2}+(y-4)^{2}=4\)

🎉 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:

Standard form: \((x-h)^{2}+(y-k)^{2}=r^{2}\), with center \((h,k)\) and radius \(r\).
The signs inside the parentheses are opposite to the coordinates of the center.
The number on the right side is \(r^{2}\), so take its square root to get the radius.
Complete the square on both variables to rewrite \(x^{2}+y^{2}+Dx+Ey+F=0\) in standard form.