Equation of a Circle: Geometry Math Quiz – PDF Download
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
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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 \((x+6)^{2}+(y-3)^{2}=25\)?
AIt is inside the circle
BIt is on the circle
CIt is outside the circle
DIt 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!
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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.
