SAT Math: Practice Questions-Additional topics in math-Circle equations

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Question

A circle has center C at (1,1) and radius 2. Which of the following is an equation of this circle?

  1. (\(x\)+1)2+(\(y\)+1)2=2
  2. (\(x\)+1)2+(\(y\)+1)2=4
  3. (\(x\)-1)2+(\(y\)-1)2=2
  4. (\(x\)-1)2+(\(y\)-1)2=4
Answer/Explanation

Ans: D

Question

\(x\)2-10\(x\)+\(y\)2+6\(y\)=2

The graph in the \(xy\)-plane of the equation above is a circle. What are the coordinates of the center of the circle?

  1. (-5,-3)
  2. (-5,3)
  3. (5,-3)
  4. (5,3)
Answer/Explanation

Ans: C

Question

\(x\)2-6\(x\)+\(y\)2-8\(y\)=0

The graph of the given equation in the \(xy\)-plane is a circle. What is the radius of the circle? 

  1. 2
  2. 3
  3. 4
  4. 5
Answer/Explanation

Ans: D

Question

In the \(xy\)-plane, a circle with radius 2 has center (0,0). Which of the following is a equation of the circle?

  1. \(x\)2+\(y\)2=2
  2. \(x\)2+\(y\)2=4
  3. \(x\)2-\(y\)2=2
  4. \(x\)2-\(y\)2=4
Answer/Explanation

Ans: B

Question

In the \(xy\)-plane, the points (-3, 10) and (3, 10) are endpoints of the diameter of a circle. Which equation represents this circle? 

  1. \(x\)2+(\(y\)-10)2=9
  2. (\(x\)+3)2+\(y\)2=36
  3. (\(x\)+3)2+(\(y\)-10)2=9
  4. (\(x\)+3)2+(\(y\)-10)2=36
Answer/Explanation

Ans: A

Question

\((x + 3)^{2} + (y – 7)^{2} = 100\)
In the \(xy\)-plane, the graph of the given equation is a circle. Which point \((x, y)\) lies on the circle? 

  1. (3, -4)
  2. (3, -1)
  3. (3, 1)
  4. (3, 4)
Answer/Explanation

Ans: B

Question

\(x^2 – 8x + y^2 – 10y = 40\)
In the \(xy\)-plane, the graph of the given equation is a circle. What is the radius of this circle?

Answer/Explanation

Ans: 9

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