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Eleventh Grade (Grade 11) Circles Questions

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Grade 11 Circles
If the points (1, 2) and (-5, 2) are endpoints of a diameter of a given circle, what is the equation of this circle?
  1. [math] (x-1)^2 + (y-2)^2 = 1 [/math]
  2. [math] (x+5)^2 + (y-2)^2 = 9 [/math]
  3. [math] (x+2)^2 + (y-2)^2 = 9 [/math]
  4. [math] (x+3)^2 + y(-1)^2 = 3 [/math]
Grade 11 Circles CCSS: HSG-GPE.A.1
What is the center and radius of the circle given by the following equation?
[math] x^2 + y^2 - 18x + 6y + 65 = 0 [/math]
  1. [math] "Center": (18, -6), \ "Radius": 65 [/math]
  2. [math] "Center": (9,-3), \ "Radius": 5 [/math]
  3. [math] "Center": (0,0), \ "Radius": sqrt(65) [/math]
  4. [math] "Center": (-9,3), \ "Radius": 25 [/math]
Grade 11 Circles
Write an equation for a circle if the endpoints of a diameter are at (1,1) and (1,-9).
  1. [math](x-1)^2+(y+4)^2=5[/math]
  2. [math](x-1)^2+(y+4)^2=25[/math]
  3. [math](x+1)^2+(y-4)^2=5[/math]
  4. [math](x+1)^2+(y-4)^2=25[/math]
Grade 11 Circles
Write an equation for the circle with center (2,1) that passes through (2,4).
  1. [math](x-2)^2+(y-1)^2=9[/math]
  2. [math](x-2)^2+(y-1)^2=3[/math]
  3. [math](x+3)^2+(y+1)^2=9[/math]
  4. [math](x+3)^2+(y+1)^2=3[/math]
Grade 11 Circles CCSS: HSG-GPE.A.1
What is the center and radius of the circle given by the following equation?
[math]x^2 + y^2 -2x +10y + 22 = 0 [/math]
  1. [math]"Center": (0, 0), \ "radius": sqrt(22)[/math]
  2. [math]"Center": (-2, 10), \ "radius": sqrt(22)[/math]
  3. [math]"Center": (1,-5), \ "radius": 2[/math]
  4. [math]"Center":(1,-5), \ "radius": 4[/math]
Grade 11 Circles CCSS: HSG-GMD.A.1

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Rearranging the equation from the previous step, we find that [math]C = 2 pi r[/math], which is the formula for the circumference of a circle. If we had started with a circle such that [math]d!=1[/math], would we have been able to derive the correct formula? Why or why not?
  1. No, a circle with a larger or smaller diameter would have had a larger or smaller circumference, and so the value found in step H would have been different.
  2. No, a circle with [math]d!=1[/math] would also have [math]r!=1/2[/math], and so the formula would be different.
  3. Yes, because other calculations would be performed to compensate for this, and thus arrive at the correct formula.
  4. Yes, since the ratio of a circle's diameter to its circumference is always the same, it doesn't matter what the length of the original circle's diameter is.
Grade 11 Circles CCSS: HSG-GMD.A.1

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Thus far, only a circle of radius 1/2 was used. Which of the following formulas would correctly relate this circle with a new circle of unknown circumference, C, and radius, r. Why?
  1. [math]C/pi = r/(1/2)[/math] because all circles are similar.
  2. [math]C=1/2 r pi[/math] since the new circle will depend on the measurements of the circle already investigated.
  3. [math]C/2 = pi r^2[/math] because the area of a circle is related to its circumference.
  4. [math]C = npi, r=n/2[/math] since the new circle's circumference and radius will depend upon the number of sides of an inscribed regular polygon.
Grade 11 Circles CCSS: HSG-GMD.A.1

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Grade 11 Circles CCSS: HSG-GMD.A.1

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As the number of sides continues to increase, will the value of the perimeter continue to increase without bound? Or is it approaching some value? Why?
  1. The perimeter value will continue to increase without bound, because the number of sides will keep increasing.
  2. The perimeter value will continue to increase without bound, because n is increasing at a faster rate than a is decreasing.
  3. The perimeter value will approach a certain value, since it is bounded by the circumference of the circle. The value seems to be [math]pi[/math].
  4. The perimeter value will approach a certain value, because as n increases, a decreases. The value seems to be 4.
Grade 11 Circles CCSS: HSG-GMD.A.1

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Grade 11 Circles CCSS: HSG-GMD.A.1

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Grade 11 Circles CCSS: HSG-GMD.A.1

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Grade 11 Circles CCSS: HSG-GMD.A.1

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Grade 11 Circles
Given the equation of a circle, [math](x-3)^2+(y+5)^2=10[/math], what is the circle's radius?
  1. [math]5[/math]
  2. [math]100[/math]
  3. [math]sqrt5[/math]
  4. [math]sqrt10[/math]
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