Circle equation translations (ACT/SAT/PSAT 8/9/10). Game on.

Circle equation translations (ACT/SAT/PSAT 8/9/10) is a grade 10 math skill aligned to Common Core standard HSG.GPE.A.1: derive the equation of a circle of given center and radius using the Pythagorean Theorem; complete the square to find the center and radius of a circle given by an equation. Below are 8 practice questions with answers and step-by-step explanations, drawn from the 10 circle equation translations (act/sat/psat 8/9/10) problems our math games drill.

CCSS HSG.GPE.A.110 questions in the bank
Kickoff

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Warm-upeasy

The equation (x−2)2+(y+1)2=16(x - 2)^2 + (y + 1)^2 = 16 represents Circle A. Circle B is obtained by shifting Circle A down 33 units in the coordinate plane. Which of the following equations represents Circle B?

Circle A has center (2,−1)(2, -1) and radius 44. Shifting down 33 moves the center to (2,−4)(2, -4), so Circle B is (x−2)2+(y+4)2=16(x - 2)^2 + (y + 4)^2 = 16.

Mid-gameeasy

The equation x2+(y−6)2=64x^2 + (y - 6)^2 = 64 represents Circle A. Circle B is obtained by shifting Circle A down 66 units in the coordinate plane. Which of the following equations represents Circle B?

Circle A has center (0,6)(0, 6) and radius 88. Shifting down 66 moves the center to the origin, so Circle B is x2+y2=64x^2 + y^2 = 64.

Mid-gameeasy

The equation (x−6)2+y2=81(x - 6)^2 + y^2 = 81 represents Circle A. Circle B is obtained by shifting Circle A left 66 units in the coordinate plane. Which of the following equations represents Circle B?

Circle A has center (6,0)(6, 0) and radius 99. Shifting left 66 moves the center to the origin, so Circle B is x2+y2=81x^2 + y^2 = 81.

Mid-gameeasy

The equation (x−3)2+(y+1)2=9(x - 3)^2 + (y + 1)^2 = 9 represents Circle A. Circle B is obtained by shifting Circle A up 44 units in the coordinate plane. Which of the following equations represents Circle B?

Circle A has center (3,−1)(3, -1) and radius 33. Shifting up 44 moves the center to (3,3)(3, 3), so Circle B is (x−3)2+(y−3)2=9(x - 3)^2 + (y - 3)^2 = 9.

Mid-gamemedium

The equation (x−4)2+(y−2)2=36(x - 4)^2 + (y - 2)^2 = 36 represents Circle A. Circle B is obtained by shifting Circle A left 55 units in the coordinate plane. Which of the following equations represents Circle B?

Circle A has center (4,2)(4, 2) and radius 66. Shifting left 55 moves the center to (−1,2)(-1, 2), so Circle B is (x+1)2+(y−2)2=36(x + 1)^2 + (y - 2)^2 = 36.

Mid-gamemedium

The equation (x−1)2+(y+4)2=49(x - 1)^2 + (y + 4)^2 = 49 represents Circle A. Circle B is obtained by shifting Circle A up 66 units in the coordinate plane. Which of the following equations represents Circle B?

Circle A has center (1,−4)(1, -4) and radius 77. Shifting up 66 moves the center to (1,2)(1, 2), so Circle B is (x−1)2+(y−2)2=49(x - 1)^2 + (y - 2)^2 = 49.

Mid-gamemedium

The equation (x+5)2+(y−3)2=25(x + 5)^2 + (y - 3)^2 = 25 represents Circle A. Circle B is obtained by shifting Circle A right 22 units in the coordinate plane. Which of the following equations represents Circle B?

Circle A has center (−5,3)(-5, 3) and radius 55. Shifting right 22 moves the center to (−3,3)(-3, 3), so Circle B is (x+3)2+(y−3)2=25(x + 3)^2 + (y - 3)^2 = 25.

Buzzer beatermedium

The equation x2+(y+2)2=16x^2 + (y + 2)^2 = 16 represents Circle A. Circle B is obtained by shifting Circle A down 55 units in the coordinate plane. Which of the following equations represents Circle B?

Circle A has center (0,−2)(0, -2) and radius 44. Shifting down 55 moves the center to (0,−7)(0, -7), so Circle B is x2+(y+7)2=16x^2 + (y + 7)^2 = 16.

Overtime

2 more. Played, not assigned.

The rest of the bank lives inside live head-to-head matches — the placement test finds the right starting difficulty.

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Tests that cover circle equation translations (act/sat/psat 8/9/10):
NAEPPSAT 8/9SATNY State MathNC EOG/EOC
Reporting domains for this skill
SAT All grades: Geometry and TrigonometryACT All grades: Preparing for Higher MathNAEP Grade 12: Measurement and GeometryACT Aspire All grades: Preparing for Higher MathATLAS Geometry: CirclesATLAS Geometry: Expressing Geometric Properties with Equations
More Grade 10 skills
Circle diameter endpoints to radius (SAT)Two-event conditional probability word problems (SAT)Advanced area formulasPossible coordinates on a circle (SAT)Normal distribution basicsUnit circle trig values (SAT)Equation of a circleMidpoint formulaAll Grade 10 practice →

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