Deriving and Using the Equation of a Circle
Authored by Barbara White
Mathematics
9th - 10th Grade
CCSS covered
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20 questions
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1.
MULTIPLE CHOICE QUESTION
1 min • 1 pt
What is the radius of a circle whose equation is
(x + 5)2 + (y – 3)2 = 16?
2 units
4 units
8 units
16 units
Tags
CCSS.HSG.GPE.A.1
2.
MULTIPLE CHOICE QUESTION
5 mins • 1 pt
What is the center of a circle whose equation is
x2+ y2 – 12x – 2y + 12 = 0?
(–12, –2)
(6, 1)
(-2, 1)
(12, 2)
Tags
CCSS.HSG.GPE.A.1
3.
MULTIPLE CHOICE QUESTION
3 mins • 1 pt
Mrs. Culland is finding the center of a circle whose equation is x2 + y2 + 6x + 4y – 3 = 0 by completing the square. Her work is shown.
x2 + y2 + 6x + 4y – 3 = 0
x2 + 6x + y2 + 4y – 3 = 0
(x2 + 6x) + (y2 + 4y) = 3
(x2 + 6x + 9) + (y2 + 4y + 4) = 3 + 9 + 4
Which completes the work correctly?
(x – 3)2 + (y – 2)2 = 42, so the center is (3, 2).
(x + 3)2 + (y + 2)2 = 42, so the center is (3, 2).
(x – 3)2 + (y – 2)2= 42, so the center is (–3, –2).
(x + 3)2 + (y + 2)2 = 42, so the center is (–3, –2).
Tags
CCSS.HSG.GPE.A.1
4.
MULTIPLE CHOICE QUESTION
1 min • 1 pt
In the diagram, a circle centered at the origin, a right triangle, and the Pythagorean theorem are used to derive the equation of a circle, x2 + y2 = r2.
If the center of the circle were moved from the origin to the point (h, k) and point P at (x, y) remains on the edge of the circle, which could represent the equation of the new circle?
(h + x)2 + (k + y)2 = r2
(x – h)2 + (y – k)2= r2
(k + x)2 + (h + y)2 = r2
(x – k)2 + (y – h)2 = r2
Tags
CCSS.HSG.GPE.A.1
5.
MULTIPLE CHOICE QUESTION
2 mins • 1 pt
Which equation represents a circle with a center at (–4, 9) and a diameter of 10 units?
(x – 9)2 + (y + 4)2 = 25
(x + 4)2 + (y – 9)2 = 25
(x – 9)2 + (y + 4)2 = 100
(x + 4)2 + (y – 9)2 = 100
Tags
CCSS.HSG.GPE.A.1
6.
MULTIPLE CHOICE QUESTION
3 mins • 1 pt
What is the equation of the circle, with centre (3,8) and radius 4 units?
Tags
CCSS.HSG.GPE.A.1
7.
MULTIPLE CHOICE QUESTION
15 mins • 1 pt
Find the equation of the circle with center (−8,3) and (2,−5) is on the circle?
Hint: you need to find the radius by plugging in values for four variables or use the distance formula and/or the midpoint formula.
x=
y=
h=
k=
in (x-h)2+(y-k)2=r2
(x+8)2+(y−3)2=164.5.
(x+3)2+(y−8)2=164.
(x)2+(y)2=164.
(x+8)2+(y−3)2=164.
Tags
CCSS.HSG.GPE.A.1
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